Quantum physics Books
Pan Stanford Publishing Pte Ltd Semiconductor Quantum Bits
Book SynopsisThis book highlights state-of-the-art qubit implementations in semiconductors and provides an extensive overview of this newly emerging field. Semiconductor nanostructures have huge potential as future quantum information devices as they provide various ways of qubit implementation (electron spin, electronic excitation) as well as a way to transfer quantum information from stationary qubits to flying qubits (photons). Therefore, this book unites contributions from leading experts in the field, reporting cutting-edge results on spin qubit preparation, read-out and transfer. The latest theoretical as well as experimental studies of decoherence in these quantum information systems are also provided. Novel demonstrations of complex flying qubit states and first applications of semiconductor-based quantum information devices are given, too.Trade Review"Undoubtedly the book represents the interest for scientists working in this field and related physics fields. It is not a textbook, but [a detailed study] of the suggested material is very important for postgraduate students specializing in the modern optics of nanosubjects and theorists studying quantum computer theory."—Igor A. Merkulov, University of Tennessee, USA"This book provides a timely summary of the state of the art from established groups around the world and will serve as a critical reference for researchers and students working to advance the frontier. The editors have done an excellent job in collecting and assembling the topics and authors for the most important areas."—Duncan G. Steel, University of Michigan, USATable of ContentsSpin and Charge Qubits; Qubit Control, Readout, and Transfer; Qubit Decoherence; Flying Qubits; Qubit Applications.
£133.00
World Scientific Publishing Co Pte Ltd Quantum World, The
Book SynopsisQuantum physics has, on the one hand, drastically changed our theoretical description of the physical world and has, on the other hand, revolutionized everyday life, by allowing us to build lasers, atomic clocks used in GPS, and semiconductor-based devices such as laptop computers and smartphones. The object of this book is to give a self-contained introduction to both aspects. It contains a detailed account of the foundational principles: superposition, entanglement, quantum non-locality, decoherence and measurement theory, and of some selected applications: quantum cryptography and quantum computers, cold atoms, light emitting and laser diodes, and atomic clocks. The book is aimed at a general audience and the only prerequisite is a high-school background in mathematics.Table of ContentsAn Inconvenient Principle; Secure Communications; Einstein, Bohr, and Bell; Atoms, Light, and Lasers; Cold Atoms; The Kingdom of Semiconductors; Relativistic Quantum Physics; Towards a Quantum Computer?; The Environment is Watching; Interpretations.
£48.75
The University of Chicago Press Quantum Dialogue
Book SynopsisThis work seeks to show that science is rooted not just in conversation but in disagreement, doubt and uncertainty. Mara Beller argues that it is precisely this culture of dialogue and controversy within the scientific community that fuels creativity.
£30.00
The University of Chicago Press BlackBody Theory and the Quantum Discontinuity
Book Synopsis
£35.15
The University of Chicago Press From Data to Quanta
Book SynopsisThe first comprehensive philosophical and historical account of the experimental foundations of Niels Bohr’s practice of physics.Trade Review"Perovic offers a novel and refreshingly unorthodox interpretation of Bohr's seminal contributions to quantum physics and their philosophical implications. Adopting a method of historically sensitive analysis, he argues convincingly that the great Dane came to his overarching hypotheses, including the complementarity principle, by inductive reasoning inherently based on experiments. He skillfully defends Bohr against the charges that his epistemological and methodological views were amateurish armchair philosophy. Perovic's book on Bohr's vision is recommendable from a scientific, historical, and philosophical perspective."--Helge Kragh, Niels Bohr Institute, University of CopenhagenTable of ContentsIntroduction Part 1: Preliminaries 2 From Laboratory to Theory 3 From Classical Experiments to Quantum Theory Part 2: Bohr’s Vision in Practice: the Old Quantum Theory 4 Spectral Lines, Quantum States, and a Master Model of the Atom 5 The Correspondence Principle as an Intermediary Hypothesis 6 Reception 7 The Scientific Moderator Part 3: Toward Quantum Mechanics 8 Quantum Corpuscles, Quantum Waves, and the Experiments 9 The Uncertainty Principle as an Intermediary Hypothesis 10 Metaphysical Principles and Heuristic Rules 11 New Formalisms and Bohr’s Atom 12 Complementarity Established and Applied Part 4: Aftermath 13 Bohr and the “Copenhagen Orthodoxy” 14 Bohr’s Response to the Einstein-Podolsky-Rosen Argument 15 The Mature Bohr and the Rise of Slick Theory and Theoreticians Acknowledgments Bibliography Index
£38.00
University of Notre Dame Press Philosophical Consequences of Quantum Theory
Book SynopsisTrade Review"Prominent philosopher-scientists, from Abner Shimony to Paul Teller, contribute articles (some revisions of seminal publications) detailing presumptions and ambiguities of quantum measurement, written especially for the nonspecialist. Some highlights include Mermin's powerful (and amusing) 'device' to highlight the 'paradox' of quantum correlations, Linda Wessels' thorough catalog of specific implicit 'axioms' of the discussion, and Cushing's prospective overview. Other gems, including some simplified models of Bell's arguments, and a range of ontological frameworks—from realism to 'holism'—make this an urgently recommended work for all colleges." —Choice"The papers collected here demonstrate how analytic philosophy of science should be done. Quantum mechanics may be mysterious in some of its aspects, but those who wish to peddle mysticism on the basis on quantum theory would do well to stay away from this excellent collection of philosophical essays." —Canadian Philosophical Reviews"These papers, collected from a 1986 conference focusing on John S. Bell's celebrated 1964 theorem, examine the philosophical issues posed by quantum theory. The book introduces Bell's theorem so that readers can understand the papers, but it is not a technical overview of the theorem or of quantum mechanics." —Science News
£20.69
Yale University Press The Shape of a Life
Book SynopsisTrade Review“The book is an unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe"For decades, mathematician Shing-Tung Yau—a winner of the 1982 Fields Medal—has been central to the cross-fertilization between modern mathematics and physics. His work in geometry, for instance, underlies much of string theory. This volume, co-authored with science writer Steve Nadis, is an intimate account of Yau’s life”—Barbara Kiser, Nature“An eye-opening and insightful account. . . . Yau’s life story is an inspiring example of the power of education.”—Dan Eady, South China Morning Post“A real story of a remarkable mathematician and of contemporary mathematics, written with passion by one of the key players”—Peter Giblin, The Mathematical GazetteFinalist in the PROSE Awards mathematics category, sponsored by the Association of American Publishers“Yau and Nadis’s The Shape of a Life opens a window into the fascinating mind and world of today’s equivalent of Apollonius of Perga, ‘The Great Geometer’ of antiquity.”—Mario Livio, author of Brilliant Blunders"The interesting life of a remarkably influential modern mathematician."—Juan Maldacena, Institute for Advanced Study“This book tells a fascinating story of a life lived between multiple cultures—China and the West, and mathematics and physics. Yau's journey from poverty in Hong Kong to the top levels of the mathematics world was not a simple one.”—Edward Witten, Institute for Advanced Study"Candid, deep, and truly inspiring, The Shape of a Life is studded with unexpected insights into Yau's thinking. An extraordinary story about an extraordinary person."—Gish Jen, author of The Girl at the Baggage Claim: Explaining the East-West Culture Gap“The remarkable story of one of the world's most accomplished mathematicians, Shing-Tung Yau, who has made profound contributions in pure mathematics, general relativity, and string theory. Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind's irrepressible spirit of discovery.”—Brian Greene, author of The Elegant Universe
£19.00
Springer New York Quantum Mechanics Fundamentals
Book SynopsisFundamental Concepts.- The Formal Framework.- Basic Tools.- Low Dimensional Systems.- Hydrogenic Atoms.- Two-Electron Atoms.- Symmetries.- Elastic Scattering.- Inelastic Collisions.- Electrodynamics.- Systems of Identical Particles.- Interpretation.- Relativistic Quantum Mechanics.- Index.Trade ReviewJOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL (27 FEBRUARY 2004) "… [The first edition] has become one of the most used and respected accounts of quantum theory … Gottfried and Yan’s book contains a vast amount of knowledge and understanding. As well as explaining the way in which quantum theory works, it attempts to illuminate fundamental aspects of the theory … For use with a well-constructed course (and, of course, this is the avowed purpose of the book; a useful range of problems is provided for each chapter), or for the relative expert getting to grips with particular aspects of the subject or aiming for a deeper understanding, the book is certainly ideal." PHYSICS TODAY (August 2004) "…especially useful for graduate students and professors who have time to go beyond the bare essentials of a topic and explore it in depth… I would recommend the book for its lucid discussions of less familiar topics alone, but the authors do not short-change the standard subjects… I expect the second edition of Gottfried and Yan to join my library of well thumbed-through texts." From the reviews of the second edition: "The book under review offers the reader in-depth physical and mathematical understanding of quantum mechanics. The book is the second edition of Gottfried’s Quantum mechanics. … Readers’ anticipations have finally been rewarded by the second edition of the earlier book, which is a complete revision covering most of the topics and much more … . The appendix contains the values of important physical constants, some useful operator identities … . The end notes at the conclusion of each chapter contain many useful references." (Howard E. Brandt, Mathematical Reviews, Issue 2007 f)Table of ContentsFundamental Concepts / The Formal Framework / Basic Tools / Low Dimensional Systems / Hydrogenic Atoms / Two-Electron Atoms / Symmetries / Elastic Scattering / Inelastic Collisions / Electrodynamics / Systems of Identical Particles / Interpretation / Relativistic Quantum Mechanics / Index.
£67.49
John Wiley & Sons Inc Modern Electromagnetic Scattering Theory with
Book SynopsisThis self-contained book gives fundamental knowledge about scattering and diffraction of electromagnetic waves and fills the gap between general electromagnetic theory courses and collections of engineering formulas.Table of ContentsPreface xi Acknowledgements xiii List of Abbreviations xv 1 Introduction 1 1.1 Scattering and Diffraction Theory 1 1.2 Books on Related Subjects 3 1.3 Concept and Outline of the Book 5 References 8 2 Fundamentals of Electromagnetic Scattering 11 2.1 Introduction 11 2.2 Fundamental Equations and Conditions 11 2.2.1 Maxwell’s Equations 12 2.2.2 Constitutive Relations 12 2.2.3 Time-harmonic Scattering Problems 19 2.3 Approximate Boundary Conditions 26 2.3.1 Impedance Boundary Conditions 26 2.3.2 Generalized (Higher-order) Impedance Boundary Conditions 31 2.3.3 Sheet Transition Conditions 32 2.4 Fundamental Properties of Time-harmonic Electromagnetic Fields 35 2.4.1 Energy Conservation and Uniqueness 35 2.4.2 Reciprocity 39 2.5 Basic Solutions of Maxwell’s Equations in Homogeneous Isotropic Media 42 2.5.1 Plane, Spherical, and Cylindrical Waves 43 2.5.2 Electromagnetic Potentials and Fields of External Currents 46 2.5.3 Tensor Green’s Function 50 2.5.4 E and H Modes 54 2.5.5 Fields with Translational Symmetry 58 2.6 Electromagnetic Formulation of Huygens’ Principle 61 2.6.1 Compact Scatterers 62 2.6.2 Cylindrical Scatterers 67 2.7 Problems 70 References 84 3 Far-field Scattering 87 3.1 Introduction 87 3.2 Scattering Cross Section 87 3.2.1 Monostatic and Bistatic, Backscattering and Forward-scattering Cross Sections, Differential, Total, Absorption, and Extinction Cross Sections 87 3.2.2 Scattering Width 91 3.2.3 Backscattering from Impedance-matched Bodies 93 3.3 Scattering Matrix 95 3.3.1 Definition 95 3.3.2 Scattering Matrix in Spherical Coordinates 97 3.3.3 Scattering Matrix in the Plane of Scattering Coordinates 99 3.4 Far-field Coefficient 101 3.4.1 Integral Representations and Far-field Conditions 102 3.4.2 Reciprocity of Scattered Fields 106 3.4.3 Forward Scattering 108 3.4.4 Cylindrical Bodies 113 3.5 Scattering Regimes 120 3.5.1 Resonant-size Scatterers 120 3.5.2 Electrically Large Scatterers 121 3.6 Electrically Small Scatterers 125 3.6.1 Physics of Dipole Scattering 126 3.6.2 Dipole Scattering in Terms of Polarizability Tensors 129 3.6.3 Magneto-dielectric Ellipsoid 131 3.6.4 Rotationally Symmetric Particles 137 3.7 Problems 148 References 162 4 Planar Interfaces 165 4.1 Introduction 165 4.2 Interface of Two Homogeneous Semi-infinite Media 167 4.2.1 Reflection and Transmission Coefficients 167 4.2.2 Brewster’s Angle 173 4.2.3 Total Internal Reflection 173 4.2.4 Interfaces with Double-negative Materials 176 4.2.5 Surface Waves 177 4.2.6 Vector Solution of Reflection and Transmission Problems 179 4.3 Arbitrary Number of Planar Layers 182 4.3.1 Solution by the Method of Characteristic Matrices 182 4.3.2 Discussion and Limiting Cases 189 4.4 Reflection and Transmission of Cylindrical and Spherical Waves 195 4.4.1 Excitation by a Linear Electric Current 195 4.4.2 Excitation by an Electric Dipole 202 4.5 A Layer between Homogeneous Half-spaces 207 4.5.1 Different Half-spaces 207 4.5.2 A PEC-backed Layer 213 4.5.3 Layer Immersed in a Homogeneous Space 215 4.6 Modeling with Approximate Boundary Conditions 224 4.6.1 Accuracy of Impedance Boundary Conditions 225 4.6.2 Accuracy of Transition Boundary Conditions 229 4.6.3 Impedance-matched Surface 232 4.7 Problems 235 References 249 5 Wedges 251 5.1 Introduction 251 5.2 The Perfectly Conducting Wedge 253 5.2.1 Formulation of Boundary Value Problem 254 5.2.2 Solution by Separation of Variables 256 5.2.3 Fields and Currents at the Edge 258 5.2.4 Reduction to an Integral Form 260 5.2.5 Special Cases 262 5.2.6 Edge-diffracted and GO Components. Diffraction Coefficient 266 5.3 Scattering from a Half-plane (Solution by Factorization Method) 271 5.3.1 Statement of the Problem 271 5.3.2 Functional Equation 273 5.3.3 Factorization and Solution 274 5.3.4 Scattered Field Far from the Edge 276 5.4 The Impedance Wedge 279 5.4.1 Boundary Value Problem, Sommerfeld’s Integrals, and Functional Equations 279 5.4.2 Normal Incidence (Maliuzhinets’ Solution) 288 5.4.3 Unit Surface Impedance 297 5.4.4 Further Exactly Solvable Cases 300 5.5 High-frequency Scattering from Impenetrable Wedges 306 5.5.1 GO Components and Surface Waves 307 5.5.2 Edge-diffracted Field, Diffraction Coefficient, and Scattering Widths 310 5.5.3 Uniform Asymptotic Approximations 316 5.5.4 GTD/UTD Formulation 319 5.6 Behavior of Electromagnetic Fields at Edges 322 5.6.1 Determining the Degree of Singularity 322 5.6.2 Analytical Structure of Meixner’s Series 328 5.7 Problems 329 References 336 6 Circular Cylinders and Convex Bodies 339 6.1 Introduction 339 6.2 Perfectly Conducting Cylinders: Separation of Variables and Series Solution 340 6.2.1 Separation of Variables 342 6.2.2 Satisfying the Boundary Conditions 342 6.2.3 Scattered Fields 343 6.2.4 Numerical Examples 345 6.3 Homogeneous Cylinders under Normal Illumination 350 6.3.1 Field Equations and Boundary Conditions 350 6.3.2 Rayleigh Series Solution 351 6.3.3 Numerical Examples 352 6.4 Watson’s Transformation and High-frequency Approximations 354 6.4.1 Watson’s Transformation 355 6.4.2 Alternative Solution by Separation of Variables 358 6.4.3 High-frequency Approximations 360 6.4.4 Surface Currents in the Penumbra Region. Fock’s Functions 369 6.5 Coated and Impedance Cylinders under Oblique Illumination 375 6.5.1 PEC Cylinder with Magneto-dielectric Coating 376 6.5.2 Impedance Cylinder 383 6.6 Extension to Generally Shaped Convex Impedance Bodies 392 6.6.1 Fock’s Principle of the Local Field in the Penumbra Region 393 6.6.2 Asymptotic Solution for the Field on the Surface of Circular Impedance Cylinders under Oblique Illumination 396 6.6.3 Fock- and GTD-type Solutions for Electrically Large Convex Impedance Bodies 398 6.7 Problems 403 References 411 7 Spheres 412 7.1 Introduction 412 7.2 Exact Solution for a Multilayered Sphere 414 7.2.1 Formulation of the Problem in Terms of Debye’s Potentials 415 7.2.2 Derivation of the Series Solution 417 7.2.3 Solution for Impedance Boundary Conditions 427 7.3 Physics of Scattering from Spheres 429 7.3.1 Classification of Scattering 430 7.3.2 Spiral Waves 436 7.3.3 Debye’s Expansions for Homogeneous Spheres 438 7.3.4 Waves in Electrically Large Homogeneous Low-absorption Spheres 442 7.4 Scattered Field in the Far Zone 463 7.4.1 Far-field Coefficient, Scattering Cross Sections, and Polarization Structure. Approximations for Electrically Large Spheres 463 7.4.2 Electrically Small Spheres: Dipole, Quasi-static, and Resonance Approximations 471 7.4.3 PEC Spheres 479 7.4.4 Core-shell Spheres 483 7.4.5 Impedance Spheres 488 7.5 Far-field Scattering from Homogeneous Spheres 493 7.5.1 Exact Solution and Limiting Cases 494 7.5.2 Electrically Small Lossy Spheres 495 7.5.3 Electrically Small Low-absorption Spheres 499 7.5.4 Electrically Large Lossy Spheres: Relation to the Impedance Sphere and the Role of Absorption 506 7.5.5 Electrically Large Low-absorption Spheres: Light Scattering from Water Droplets 513 7.6 Metamaterial Effects in Scattering from Spheres 542 7.6.1 Small Spheres 542 7.6.2 Invisibility Cloak 546 7.7 Problems 552 References 562 8 Method of Physical Optics 565 8.1 Introduction 565 8.1.1 On Numerical Techniques for Studying Scattering from Arbitrary-shaped Bodies 565 8.1.2 PO as one of the Approximate Analytical Techniques 566 8.1.3 Structure of the Chapter 567 8.2 Principles and General Solution 567 8.2.1 Principles of PO 567 8.2.2 Derivation of PO Solutions 569 8.2.3 PO for Cylindrical Bodies 573 8.3 Transmission through Apertures 575 8.3.1 PO Solution 575 8.3.2 GO Rays and Fresnel Zones 576 8.3.3 Contribution from the Rim of the Aperture: Edge-diffracted Rays 582 8.4 Scattering from Curved Surfaces 594 8.4.1 Fock’s Reflection Formula 594 8.4.2 Application to a Spherical Segment 600 8.4.3 Reflection Formula in the Far-field Region 605 8.4.4 Diffraction by an Edge in a Non-metallic Surface 609 8.5 Advantages and Limitations of Physical Optics 615 8.6 Problems 616 References 632 9 Physical Optics Solutions of Canonical Problems 634 9.1 Introduction 634 9.2 Vertices 635 9.2.1 Vertex on an Edge of a Thin Plate 637 9.2.2 Apex of a Pyramid 641 9.2.3 Tip of an Elliptic Cone 643 9.3 Electrically Large Plates 652 9.3.1 Arbitrarily Shaped Plates 653 9.3.2 Circular Disc 658 9.3.3 Polygonal Plates 663 9.3.4 Far-field Patterns of Polygonal Plates and Apertures 667 9.4 Bodies of Revolution 671 9.4.1 PO Solution for Bodies of Revolution 672 9.4.2 Imperfectly Reflecting Bodies under Axial Illumination 675 9.4.3 PEC Bodies under Oblique Illumination 677 9.4.4 Axial Backscattering 678 9.4.5 Examples 684 9.5 Problems 689 References 712 A Definitions and Useful Relations of Vector Analysis and Differential Geometry 714 A.1 Vector Algebra 714 A.2 Vector Analysis 716 A.3 Vectors and Vector Differential Operators in Orthogonal Curvilinear Coordinates 717 A.3.1 General Orthogonal Curvilinear Coordinates 717 A.3.2 Spherical Coordinates 718 A.4 Curves and Surfaces in Space 720 A.4.1 Curves 720 A.4.2 Surfaces 720 A.5 Problems 722 References 724 B Fresnel Integral and Related Functions 725 B.1 Fresnel Integral 725 B.2 Relation to the Error Function 728 B.3 Transition Functions of Uniform Theories of Diffraction 730 B.4 Problems 731 References 732 C Principles of Complex Integration 733 C.1 Introduction 733 C.2 Deforming the Integration Contour 734 C.2.1 Basic Facts about Functions of a Complex Variable 734 C.2.2 Integrals over Infinite Contours 736 C.3 Steepest Descent Method 737 C.3.1 Steepest Descent Path 738 C.3.2 Saddle Point Contribution 739 C.3.3 Pole Singularity near the Saddle Point 741 C.3.4 Further Cases 742 C.4 Problems 743 References 745 D The Stationary Phase Method 746 D.1 Introduction 746 D.2 One-dimensional Integrals 746 D.2.1 No Stationary Points on the Integration Interval 747 D.2.2 Isolated Stationary Points 748 D.2.3 Two Coalescing Stationary Points 751 D.3 Two-dimensional Integrals 756 D.3.1 Stationary Point in the Integration Domain 756 D.3.2 Stationary Point near the Boundary of the Integration Domain 758 D.3.3 Contribution from the Boundary of the Integration Domain 760 D.3.4 Kontorovich’s Formula 763 D.3.5 Integrand Vanishing on the Boundary 765 D.3.6 Summary of the Two-dimensional Stationary-phase Method 766 D.4 Problems 766 References 768 E Asymptotic Approximations of Bessel Functions of Large Argument and Arbitrary Order 770 E.1 Introduction 770 E.1.1 Basic Definitions and Properties 770 E.1.2 Large-argument Approximations (|z| â 1) 772 E.1.3 Content of the Appendix 775 E.2 Debye’s Asymptotic Approximations 776 E.2.1 Debye’s Method 776 E.2.2 WKB Approximation 778 E.2.3 Bessel Functions on the Complex 𝜈 Plane 791 E.3 Almost Equal Argument and Order 795 E.3.1 Approximations in Terms of Airy Functions 796 E.3.2 Approximations in Terms of Normalized Airy Functions 797 E.3.3 Zeros in the Neighborhood of the Points 𝜈 = ±z 798 References 799 Index 801
£122.35
John Wiley & Sons Inc Principles and Practices of Molecular Properties
Book SynopsisFocusing on spectroscopic properties of molecular systems, Quantum Modeling of Molecular Materials presents the state-of-the-art methods in theoretical chemistry that are used to determine molecular properties relevant to different spectroscopies.Table of ContentsPreface xi 1 Introduction 1 2 Quantum Mechanics 11 2.1 Fundamentals 11 2.1.1 Postulates of Quantum Mechanics 11 2.1.2 Lagrangian and Hamiltonian Formalisms 11 2.1.3 Wave Functions and Operators 18 2.2 Time Evolution of Wave Functions 22 2.3 Time Evolution of Expectation Values 25 2.4 Variational Principle 27 Further Reading 29 3 Particles and Fields 31 3.1 Microscopic Maxwell’s Equations 32 3.1.1 General Considerations 32 3.1.2 The Stationary Case 34 3.1.3 The General Case 38 3.1.4 Electromagnetic Potentials and Gauge Freedom 39 3.1.5 Electromagnetic Waves and Polarization 41 3.1.6 Electrodynamics: Relativistic and Nonrelativistic Formulations 45 3.2 Particles in Electromagnetic Fields 48 3.2.1 The Classical Mechanical Hamiltonian 48 3.2.2 The Quantum-Mechanical Hamiltonian 52 3.3 Electric and Magnetic Multipoles 57 3.3.1 Multipolar Gauge 57 3.3.2 Multipole Expansions 59 3.3.3 The Electric Dipole Approximation and Beyond 63 3.3.4 Origin Dependence of Electric and Magnetic Multipoles 64 3.3.5 Electric Multipoles 65 3.3.5.1 General Versus Traceless Forms 65 3.3.5.2 What We Can Learn from Symmetry 68 3.3.6 Magnetic Multipoles 69 3.3.7 Electric Dipole Radiation 70 3.4 Macroscopic Maxwell’s Equations 72 3.4.1 Spatial Averaging 72 3.4.2 Polarization and Magnetization 73 3.4.3 Maxwell’s Equations in Matter 77 3.4.4 Constitutive Relations 79 3.5 Linear Media 81 3.5.1 Boundary Conditions 82 3.5.2 Polarization in Linear Media 86 3.5.3 Electromagnetic Waves in a Linear Medium 92 3.5.4 Frequency Dependence of the Permittivity 96 3.5.4.1 Kramers–Kronig Relations 97 3.5.4.2 Relaxation in the Debye Model 98 3.5.4.3 Resonances in the Lorentz Model 101 3.5.4.4 Refraction and Absorption 105 3.5.5 Rotational Averages 107 3.5.6 A Note About Dimensions, Units, and Magnitudes 110 Further Reading 111 4 Symmetry 113 4.1 Fundamentals 113 4.1.1 Symmetry Operations and Groups 113 4.1.2 Group Representation 117 4.2 Time Symmetries 120 4.3 Spatial Symmetries 125 4.3.1 Spatial Inversion 125 4.3.2 Rotations 127 Further Reading 134 5 Exact-State Response Theory 135 5.1 Responses in Two-Level System 135 5.2 Molecular Electric Properties 145 5.3 Reference-State Parameterizations 151 5.4 Equations of Motion 156 5.4.1 Time Evolution of Projection Amplitudes 157 5.4.2 Time Evolution of Rotation Amplitudes 159 5.5 Response Functions 163 5.5.1 First-Order Properties 166 5.5.2 Second-Order Properties 166 5.5.3 Third-Order Properties 169 5.5.4 Fourth-Order Properties 174 5.5.5 Higher-Order Properties 179 5.6 Dispersion 179 5.7 Oscillator Strength and Sum Rules 183 5.8 Absorption 185 5.9 Residue Analysis 190 5.10 Relaxation 194 5.10.1 Density Operator 195 5.10.2 Liouville Equation 196 5.10.3 Density Matrix from Perturbation Theory 200 5.10.4 Linear Response Functions from the Density Matrix 201 5.10.5 Nonlinear Response Functions from the Density Matrix 204 5.10.6 Relaxation in Wave Function Theory 204 5.10.7 Absorption Cross Section 207 5.10.8 Einstein Coefficients 210 Further Reading 211 6 Electronic and Nuclear Contributions to Molecular Properties 213 6.1 Born–Oppenheimer Approximation 213 6.2 Separation of Response Functions 216 6.3 Molecular Vibrations and Normal Coordinates 221 6.4 Perturbation Theory for Vibrational Wave Functions 225 6.5 Zero-Point Vibrational Contributions to Properties 227 6.5.1 First-Order Anharmonic Contributions 227 6.5.2 Importance of Zero-Point Vibrational Corrections 231 6.5.3 Temperature Effects 234 6.6 Pure Vibrational Contributions to Properties 235 6.6.1 Perturbation Theory Approach 235 6.6.2 Pure Vibrational Effects from an Analysis of the Electric-Field Dependence of the Molecular Geometry 238 6.7 Adiabatic Vibronic Theory for Electronic Excitation Processes 244 6.7.1 Franck–Condon Integrals 248 6.7.2 Vibronic Effects in a Diatomic System 250 6.7.3 Linear Coupling Model 252 6.7.4 Herzberg–Teller Corrections and Vibronically Induced Transitions 252 Further Reading 253 7 Approximate Electronic State Response Theory 255 7.1 Reference State Parameterizations 255 7.1.1 Single Determinant 255 7.1.2 Configuration Interaction 263 7.1.3 Multiconfiguration Self-Consistent Field 266 7.1.4 Coupled Cluster 268 7.2 Equations of Motion 271 7.2.1 Ehrenfest Theorem 271 7.2.2 Quasi-Energy Derivatives 275 7.3 Response Functions 276 7.3.1 Single Determinant Approaches 276 7.3.2 Configuration Interaction 281 7.3.3 Multiconfiguration Self-Consistent Field 281 7.3.4 Matrix Structure in the SCF, CI, and MCSCF Approximations 281 7.3.5 Coupled Cluster 285 7.4 Residue Analysis 288 7.5 Relaxation 291 Further Reading 293 8 Response Functions and Spectroscopies 295 8.1 Nuclear Interactions 296 8.1.1 Nuclear Charge Distribution 296 8.1.2 Hyperfine Structure 301 8.1.2.1 Nuclear Magnetic Dipole Moment 301 8.1.2.2 Nuclear Electric Quadrupole Moment 305 8.2 Zeeman Interaction and Electron Paramagnetic Resonance 310 8.3 Polarizabilities 317 8.3.1 Linear Polarizability 317 8.3.1.1 Weak Intermolecular Forces 321 8.3.2 Nonlinear Polarizabilities 325 8.4 Magnetizability 326 8.4.1 The Origin Dependence of the Magnetizability 328 8.4.2 Magnetizabilities from Magnetically Induced Currents 331 8.4.3 Isotropic Magnetizabilities and Pascal’s Rule 332 8.5 Electronic Absorption and Emission Spectroscopies 335 8.5.1 Visible and Ultraviolet Absorption 338 8.5.2 Fluorescence Spectroscopy 343 8.5.3 Phosphorescence 344 8.5.4 Multiphoton Absorption 347 8.5.4.1 Multiphoton Absorption Cross Sections 348 8.5.4.2 Few-State Models for Two-Photon Absorption Cross Section 350 8.5.4.3 General Multiphoton Absorption Processes 351 8.5.5 X-ray Absorption 354 8.5.5.1 Core-Excited States 355 8.5.5.2 Field Polarization 358 8.5.5.3 Static Exchange Approximation 360 8.5.5.4 Complex or Damped Response Theory 362 8.6 Birefringences and Dichroisms 364 8.6.1 Natural Optical Activity 366 8.6.2 Electronic Circular Dichroism 372 8.6.3 Nonlinear Birefringences 375 8.6.3.1 Magnetic Circular Dichroism 376 8.6.3.2 Electric Field Gradient-Induced Birefringence 379 8.7 Vibrational Spectroscopies 381 8.7.1 Infrared Absorption 381 8.7.1.1 Double-Harmonic Approximation 381 8.7.1.2 Anharmonic Corrections 383 8.7.2 Vibrational Circular Dichroism 384 8.7.3 Raman Scattering 388 8.7.3.1 Raman Scattering from a Classical Point of View 388 8.7.3.2 Raman Scattering from a Quantum Mechanical Point of View 392 8.7.4 Vibrational Raman Optical Activity 402 8.8 Nuclear Magnetic Resonance 408 8.8.1 The NMR Experiment 408 8.8.2 NMR Parameters 413 Further Reading 417 Appendicies A Abbreviations 419 B Units 421 C Second Quantization 423 C.1 Creation and Annihilation Operators 423 C.2 Fock Space 425 C.3 The Number Operator 426 C.4 The Electronic Hamiltonian on Second-Quantized Form 427 C.5 Spin in Second Quantization 429 D Fourier Transforms 431 E Operator Algebra 435 F Spin Matrix Algebra 439 G Angular Momentum Algebra 441 H Variational Perturbation Theory 445 I Two-Level Atom 451 I.1 Rabi Oscillations 452 I.2 Time-Dependent Perturbation Theory 454 I.3 The Quasi-energy Approach 455 Index 457
£137.66
John Wiley & Sons Inc Quantum Physics
Book SynopsisSince the publication of the first edition over 35 years ago, Quantum Physics has been one of the standard quantum mechanics texts for undergraduate physics majors. Its hallmarks are clear, concise exposition and a balance of theory and applications. In the 3rd Edition, the author has made numerous changes?based on feedback from teachers and students?to enhance the book''s strengths. One of the author''s important goals has been to offer teachers and students a textbook that is manageable in one semester. However, recognizing that some teachers like to go into more depth on certain topics, he has developed a web site where more detailed presentations can be found.Table of ContentsThe Emergence of Quantum Physics. Wave Particle Duality, Probability, and the Schrödinger Equation. Eigenvalues, Eigenfunctions, and the Expansion Postulate. One-Dimensional Potentials. The General Structure of Wave Mechanics. Operator Methods in Quantum Mechanics. Angular Momentum. The Schrödinger Equation in Three Dimensions and the Hydrogen Atom. Matrix Representation of Operators. Spin. Time-Independent Perturbation Theory. The Real Hydrogen Atom. Many Particle Systems. About Atoms and Molecules. Time-Dependent Perturbation Theory. The Interaction of Charged Particles with the Electromagnetic Field. Radiative Decays. Selected Topics on Radiation. Collision Theory. Entanglement and Its Implications. Physical Constants. References. Index.
£215.96
John Wiley & Sons Inc Nonlinear Optics and Quantum Electronics
Book SynopsisBased on a course of lectures for advanced students. Part 1 is devoted to an introductory treatment of general concepts and methods to be used for describing nonlinear processes. Part 2 is concerned with the application of these concepts and methods to effects and processes.Table of ContentsPartial table of contents: PART I: GENERAL CONCEPTS AND METHODS OF NONLINEAR OPTICS. Electromagnetic Fields. Classical Description. The Quantized Free Radiation Field. Interaction Between Radiation and Matter. Semiclassical Description of Nonlinear Optics. Statistical and Coherence Properties of the Radiation Field andTheir Measurement. Nonstationary Processes. PART II: EFFECTS AND PROCESSES OF NONLINEAR OPTICS. Nonlinear One-photon Processes in Lasers. Nonlinearities in Transient One-photon Processes. Nonlinearities and Qunatum Phenomena in Transient One-photonProcesses. Multiphoton Absorption and Emission. Generation of Harmonics and Sum and Difference Frequencies. Parametric Amplification and Oscillation. Stimulated Raman Scattering. Optical Bistability. APPENDIX A: Compilation of Quantum-Theoretical Definitions andRelations. General References. Index.
£268.15
John Wiley & Sons Inc Resonances Instability and Irreversibility Volume
Book SynopsisIn Resonances, Instability, and Irreversibility: The LiouvilleSpace Extension of Quantum Mechanics T. Petrosky and I. Prigogine Unstable Systems in Generalized Quantum Theory E. C. G. Sudarshan, Charles B. Chiu, and G. Bhamathi Resonances and Dilatation Analyticity in Liouville Space Erkki J. Brandas Time, Irreversibility, and Unstable Systems in QuantumPhysics E. Eisenberg and L. P. Horwitz Quantum Systems with Diagonal Singularity I. Antoniou and Z. Suchanecki Nonadiabatic Crossing of Decaying Levels V. V. and Vl. V. Kocharovsky and S. Tasaki Can We Observe Microscopic Chaos in the Laboratory? Pierre Gaspard Proton Nonlocality and Decoherence in Condensed Matter --Predictions and Experimental Results C. A. Chatzidimitriou-Dreismann We are at a most interesting moment in the history of science.Classical science emphasized equilibrium, stabilitTable of ContentsThe Liouville Space Extension of Quantum Mechanics (T. Petrosky& I. Prigogine). Unstable Systems in Generalized Quantum Theory (E. Sudarshan, etal.). Resonances and Dilation Analyticity in Liouville Space (E.Bandas). Time, Irreversibility and Unstable Systems in Quantum Physics (E.Eisenberg & L. Horwitz). Quantum Systems with Diagonal Singularity (I. Antoniou & Z.Suchanecki). Nonadiabatic Crossing of Decaying Levels (V. Kocharovsky, etal.). Can We Observe Microscopic Chaos in the Laboratory? (P. Gaspard) Proton Nonlocality and Decoherence in CondensedMatter-Predictions and Experimental Results (C.Chatzidimitriou-Dreismann). Indexes.
£375.26
John Wiley & Sons Inc New Methods in Computational Quantum Mechanics
Book SynopsisThe use of quantum chemistry for the quantitative prediction of molecular properties has long been frustrated by the technical difficulty of carrying out the needed computations. In the last decade there have been substantial advances in the formalism and computer hardware needed to carry out accurate calculations of molecular properties efficiently. These advances have been sufficient to make quantum chemical calculations a reliable tool for the quantitative interpretation of chemical phenomena and a guide to laboratory experiments. However, the success of these recent developments is not well known outside the community of practitioners. In order to make the larger community of chemical physicists aware of the current state of the subject, this self-contained volume of Advances in Chemical Physics surveys a number of the recent accomplishments in computational quantum chemistry. Supplemented with more than 150 illustrations, this volume provides evaluations of a broad range of metTable of ContentsQuantum Monte Carlo Methods in Chemistry (D. Ceperley & L.Mitas). Monte Carlo Methods for Real-Time Path Integration (C. Mak & R.Egger). The Redfield Equation in Condensed-Phase Quantum Dynamics (W.Pollard, et al.). Path-Integral Centroid Methods in Quantum Statistical Mechanicsand Dynamics (G. Voth). Multiconfigurational Perturbation Theory: Applications inElectronic Spectroscopy (B. Roos, et al.). Electronic Structure Calculations for Molecules ContainingTransition Metals (P. Siegbahn). The Interface Between Electronic Structure Theory and ReactionDynamics by Reaction Path Methods (M. Collins). Algebraic Models in Molecular Spectroscopy (S. Oss). Tight-Binding Molecular Dynamics Studies of Covalent Systems (C.Wang & K. Ho). Perspectives on Semiempirical Molecular Orbital Theory (W.Thiel). Indexes.
£193.46
John Wiley & Sons Inc Applied Quantum Mechanics
Book SynopsisQuantum mechanics is vitally important in the study and design of semiconductor devices and in the emerging field of quantum computing. Whereas most quantum mechanics books are written for a physics audience, this book is aimed at electrical engineers and materials scientists.Table of ContentsIntroduction. PART I: FOUNDATIONS. 1. Particles and Waves. 2. Probability Amplitudes. 3. The Origins of Quantum Mechanics. 4. The Schrödinger Equation and Wave Packet Solutions. 5. Operators, Expectation Values, and Ehrenfest's Theorem. PART II: THE TIME-INDEPENDENT SCHRÖDINGER EQUATION. 6. Eigenfunctions and Eigenvalues. 7. Piecewise Constant Potentials: I. 8. Piecewise Constant Potentials: II. PART III: THE SIMPLE HARMONIC OSCILLATOR. 9. The Simple Harmonic Oscillator I. 10. The Simple Harmonic Oscillator II: Operators. 11. The Simple Harmonic Oscillator III: Wave Packet Solutions. 12. The Quantum LC Circuit. PART IV: USEFUL APPROXIMATIONS. 13. Overview of Approximate Methods for Eigenfunctions. 14. The WKB Approximation. 15. The Variational Method. 16. Finite Basis Approximation. PART V: THE TWO-LEVEL SYSTEM. 17. The Two-level System with Static Coupling. 18. Th e Two-level System with Dynamical Coupling. 19. Coupld Two-level System and Simple Harmonic Oscillator. PART VI: QUANTUM SYSTEMS WITH MANY DEGREES OF FREEDOM. 20. Problems in More than One Dimension. 21. Electromagnetic Field Quantization I: Resonator Fields. 22. Electromagnetic Field Quantization II: Free-space Fields. 23. The Density of States. 24. The Golden Rules: The Calculation of Transition Raes. PART VII: STATISTICAL MECHANICS. 25. Basic Concepts of Statistical Mechanics. 26. Microscopic Quantum Systems in Equilibrium with a Reservoir. 27. Statistical Models Applied to Metals and Semiconductors. PART VIII: HYDROGEN ATOM, HELIUM ATOM, AND MOLECULAR HYDROGEN. 28. The Hydrogen Atom I: The Classical Problems. 29. The Hydrogen Atom II: The Quantum Problem. 30. The Hydrogen Atom III: Applications. 31. Two-Electron Atoms and Ions. 32. Molecular Hydrogen I: H2+ and H2 Electronic Orbitals. 33. Molecular Hydrogen II: Vibrational and Rotational States. PART IX: APPENDICES. Appendix A: Gaussian Integrals. Appendix B: The Fourier Transform of a Plane Wave. Appendix C: The Probability Flux. Appendix D: The Cascaded Matrix Method. Appendix E: The Creation Operator Raises the Index. Appendix F: Canonical Quantization. Appendix G: Wave Packet Incident on a "Gentle" Potential Step. Appendix H: The WKB Representation for Allowed Regions. Appendix I: The WKB Representation for Forbidden Regions. Appendix J: Matrix Elements for the Quartic Well. Appendix K: Normalization, and the Unity Operator. Appendix L: The Density Operator and Density Matrix. Appendix M: The Two-level System Hamiltonian. Appendix N: Thinking about Dirac Notation. Appendix O: Coordinate Rotation and the Two-dimensional SHO. Appendix P: Conservation Law for the Electromagnetic Energy Density. Appendix Q: The Grand Partition Function. Appendix R: Analytic Results for Metals Properties. Appendix S: Saha Equilibrium for a Hydrogen Plasma. Appendix T: Nuclear Magnetic Resonance. Appendix U: The Atomic Force Microscope. Appendix V: The Heisenberg Picture. References. Index.
£136.76
John Wiley & Sons Inc Quantum Electronics
Book SynopsisThis Third Edition of the popular text, while retaining nearly all the material of the previous edition, incorporates material on important new developments in lasers and quantum electronics. Covers phase-conjugate optics and its myriad applications, the long wavelength quaternary semiconductor laser, and our deepened understanding of the physics of semiconductor lasers--especially that applying to their current modulations and limiting bandwidth, laser arrays and the related concept of supermodes, quantum well semiconductor lasers, the role of phase amplitude coupling in laser noise, and free-electron lasers. In addition, the chapters on laser noise and third-order nonlinear effects have been extensively revised.Table of ContentsBasic Theorems and Postulates of Quantum Mechanics. Some Solutions of the Time-Independent Schrödinger Equation. Matrix Formulation of Quantum Mechanics. Lattice Vibrations and Their Quantization. Electromagnetic Fields and Their Quantization. The Propagation of Optical Beams in Homogeneous and Lenslike Media. Optical Resonators. Interaction of Radiation and Atomic Systems. Laser Oscillation. Some Specific Laser Systems. Semiconductor Diode Lasers. Quantum Well Lasers. The Free-Electron Laser. The Modulation of Optical Radiation. Coherent Interactions of a Radiation Field and an Atomic System. Introduction to Nonlinear Optics--Second-Harmonic Generation. Parametric Amplification, Oscillation, and Fluorescence. Third-Order Optical Nonlinearities--Stimulated Raman and Brillouin Scattering. Phase-Conjugate-Optics and Photorefractive Beam Coupling. Q-Switching and Mode Locking of Lasers. Noise and Spectra of Laser Amplifiers and Oscillators. Guided Wave Optics--Propagation in Optical Fibers. Appendices. Index.
£232.16
John Wiley & Sons Inc Quantum Theory of Solids
Book SynopsisA modern presentation of theoretical solid state physics that builds directly upon Kittela s Introduction to Solid State Physics. Treats phonon, electron, and magnon fields, culminating in the BCS theory of superconductivity. Considers Fermi surfaces and electron wave functions and develops the group theoretical description of Brillouin zones.Table of ContentsMathematical Introduction. Acoustic Phonons. Plasmons, Optical Phonons, and Polarization Waves. Magnons. Fermion Fields and the Hartree-Forck Approximation. Many-Body Techniques and the Electron Gas. Polarons and the Electron-Phonon Interaction. Superconductivity. Bloch Funcations--General Properties. Brillouin Zones and Crystal Symmetry. Dynamics of Electronics in a Magnetic Field: de Hass-van AlphenEffect and Cyclotron Resonance. Magnetoresistance. Calculation of Energy Bands and Fermi Surfaces. Semiconductor Crystals: I. Energy Bands, Cyclotron Resonance andImpurity States. Semiconductor Crystals: II. Optical Absorption and Excitons. Electrodynamics of Metals. Acoustic Attenuation in Metals. Theory of Alloys. Correlation Functions and Neutron Diffraction by Crystals. Recoilless Emission. Green's Functions--Application to Solid State Physics. Appendixes.
£135.80
John Wiley & Sons Inc Angular Momentum
Book SynopsisDesigned as a learning tool for those with limited background in quantum mechanics, this book provides comprehensive coverage of angular momentum in quantum mechanics and its applications to chemistry and physics.Table of ContentsAngular Momentum Operators and Wave Functions. Coupling of Two Angular Momentum Vectors. Transformation under Rotation. The Coupling of More than Two Angular Momentum Vectors. Spherical Tensor Operators. Energy-level Structure and Wave Functions of a Rigid Rotor. Appendix: Computer Programs for 3J, 6J, and 9J Symbols. Index.
£152.06
John Wiley & Sons Inc Quantum Mechanics
Book SynopsisRapid advances in quantum optics, atomic physics, particle physics and other areas have been driven by fantastic progress in instrumentation (especially lasers) and computing technology as well as by the ever-increasing emphasis on symmetry and information concepts-requiring that all physicists receive a thorough grounding in quantum mechanics.Table of ContentsIntroduction to Quantum Mechanics. Wave Packets, Free Particle Motion, and the Wave Equation. The Schrödinger Equation, the Wave Function, and Operator Algebra. The Principles of Wave Mechanics. The Linear Harmonic Oscillator. Sectionally Constant Potentials in One Dimension. The WKB Approximation. Variational Methods and Simple Perturbation Theory. Vector Spaces in Quantum Mechanics. Eigenvalues and Eigenvectors of Operators, the Uncertainty Relations, and the Harmonic Oscillator. Angular Momentum in Quantum Mechanics. Spherically Symmetric Potentials. Scattering. The Principles of Quantum Dynamics. The Quantum Dynamics of a Particle. The Spin. Rotations and Other Symmetry Operations. Bound-State Perturbation Theory. Time-Dependent Perturbation Theory. The Formal Theory of Scattering. Identical Particles. Applications to Many-Body Systems. Photons and the Electromagnetic Field. Relativistic Electron Theory. Appendix. References. Index.
£234.86
Harvard University Press Qbism The Future of Quantum Physics
Book SynopsisShort for Quantum Bayesianism, QBism adapts conventional features of quantum mechanics in light of a revised understanding of probability. Using commonsense language, without the equations or weirdness of conventional quantum theory, Hans Christian von Baeyer clarifies the meaning of quantum mechanics and suggests a new approach to general physics.Trade ReviewHans Christian von Baeyer has done a wonderful job with this book. I’ve been fortunate enough to learn QBism twice in my life. The first time, it was the hard way, as colleagues and I battled out every nuance of the forming theory, always testing and retesting, tearing down and reconstructing—we had to turn our world upside down to get there. But the second time was pure pleasure as I learned the subject afresh from Professor von Baeyer’s masterful articulation of it. So many of his turns of phrase are insightful gems I never could have formulated myself. Now for the first time I believe I know how to teach the subject, and there is no better understanding one can have than that! -- Christopher A. Fuchs, Professor of Physics, University of Massachusetts Boston, and key architect of QBismPhysicists all agree on how to do calculations using quantum mechanics and disagree markedly on what those calculations really mean. With his customary humor and elegance, Professor von Baeyer walks us through one of the more recent attempts to understand the mysterious world inside the atom. -- James Trefil, Professor of Physics, George Mason University, and the author of Science in World HistoryQBism remains controversial, but scientifically inclined readers will share von Baeyer’s enthusiasm and come away with a feeling, if not a deep understanding, of quantum phenomena that doesn’t require suspension of disbelief. * Kirkus Reviews *Von Baeyer offers a sensible approach to this seemingly esoteric world…He has an enthusiastic presentation and style that sweeps the reader along into the world of quantum physics and makes sense of it. -- Ralph Peterson * Manhattan Book Review *QBism should be applauded as a breeding ground of ideas for multiple disciplines including physics, philosophy, and mathematics, and von Baeyer’s book offers an account accessible to all…[It] provide[s] an outstanding introduction to two of the key components of QBism (quantum theory and subjective Bayesianism), and places the reader into the mind of the QBist in a way that will aid the ongoing debate over its merit. It is a worthwhile read. -- Kelvin J. McQueen * Quantum Times *
£32.36
Harvard University Press The Perfect Wave
Book SynopsisAlmost weightless and able to pass through the densest materials with ease, neutrinos may offer answers to questions ranging from relativity and quantum mechanics to more radical theories about dark energy and supersymmetry. Heinrich Päs serves as our fluent guide to a particle world that tests the boundaries of space, time, and human knowledge.Trade ReviewSome science books are good because they tell you a lot about science. Some are good because they present their examples and argument in very well written prose. A few do both. The Perfect Wave is one of the few… I can highly recommend The Perfect Wave as a pleasant and provocative way to gain insight into the way physicists think, and into the way the universe (probably) works. -- John Gribbin * Wall Street Journal *Päs for his part, places neutrinos within the broader context of contemporary high theory and delves deeper into the science. Physics buffs will relish his explanations, and not just of established ideas such a the seesaw mechanism. Neutrinos, Päs explains, may offer a way to probe the extra dimensions of space postulated by some ‘theories of everything.’ The puny particles’ weirdness, it seems, knows no end. * The Economist *The ghostly neutrino—a mutable, almost massless particle that can pass through dense substances—stars in this scientific history. Theoretical physicist Heinrich Päs surfs the decades of dazzling research since Wolfgang Pauli first posited the particle in 1930. Päs revisits key theorists such as Ettore Majorana, and lays out the work of groundbreaking labs from Los Alamos in New Mexico, where Fred Reines and Clyde Cowan first detected neutrinos in the early 1950s, to today’s vast IceCube neutrino observatory in Antarctica. * Nature *Written by one of the world’s leading experts in the field…Heinrich Päs’ book guides the reader through some difficult territory, covering the historical and philosophical developments that led to our understanding of the neutrino today. It is a peculiar route that navigates via such topics as the ancient Greek and magic mushrooms. Plus of course the obligatory cat that is simultaneously alive and dead… Though this book is written in simple language, don’t expect an easy read. There are some highly challenging ideas to get your head around—but it is worth making the effort. -- Paul Sutherland * BBC Sky at Night *Takes readers for a wild ride in pursuit of the neutrino—part ghost, part outlaw, part Holy Grail to theoretical physicists… From vast laboratories deep underground to the cutting edge Ice Cube Neutrino Observatory nearing completion in frigid Antarctica, Päs reveals the ‘world of madmen, dreamers, and visionaries’ who pursue the neutrino and its place in theoretical physics. * Publishers Weekly *Entertaining and evocative, Päs has written a breezy, readable account of particle physics, especially neutrino physics, in a lucid, lively narrative. -- Sandip Pakvasa, Professor of Physics and Astronomy, University of Hawai‘i at Mānoa
£39.06
Harvard University Press The Probability Map of the Universe
Book SynopsisDavid Albert’s 2000 book Time and Chance attempts to account for some of the most intractable problems in theoretical physics, in particular those arising from the direction of time. This collection assembles essays exploring and debating Albert’s ideas, now recognized as among the most important recent contributions to the philosophy of science.Trade ReviewThis volume will constitute a significant, serious contribution to a range of debates spanning philosophy of physics, general philosophy of science, metaphysics, and epistemology. The contributors are all first-rate philosophers, their essays uniformly excellent in quality. -- Edward J. Hall, Harvard UniversityAlbert’s Time and Chance sparked a lively debate about the deep origins of time asymmetry, such as why do we know more about the past than future? The Probability Map of the Universe is a fantastic entry into this debate. It is focused yet broad, has overlap without redundancy, and is chock full of engaging contributions by experts. -- Craig Callender, University of California, San Diego
£32.26
Princeton University Press Diffusion Quantum Theory and Radically Elementary
Book SynopsisExplains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. This book shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis.Table of Contents*FrontMatter, pg. i*Contents, pg. vii*Preface, pg. ix*Chapter One. Introduction: Diffusive Motion and Where It Leads, pg. 1*Chapter Two. Hypercontractivity, Logarithmic Sobolev Inequalities, and Applications: A Survey of Surveys, pg. 45*Chapter Three. Ed Nelson's Work in Quantum Theory, pg. 75*Chapter Four Symanzik, Nelson, and Self-Avoiding Walk, pg. 95*Chapter Five. Stochastic Mechanics: A Look Back and a Look Ahead, pg. 117*Chapter Six. Current Trends in Optimal Transportation: A Tribute to Ed Nelson, pg. 141*Chapter Seven. Internal Set Theory and Infinitesimal Random Walks, pg. 157*Chapter Eight. Nelson's Work on Logic and Foundations and Other Reflections on the Foundations of Mathematics, pg. 183*Chapter Nine. Some Musical Groups: Selected Applications of Group Theory in Music, pg. 209*Chapter Ten. Afterword, pg. 229*Appendix A. Publications by Edward Nelson, pg. 233*Index, pg. 241
£63.75
Princeton University Press Elementary Particle Physics in a Nutshell
Book SynopsisThe new experiments underway at the Large Hadron Collider at CERN in Switzerland may significantly change our understanding of elementary particle physics and, indeed, the universe. Suitable for first-year graduate students and advanced undergraduates, this textbook provides an introduction to the field.Trade Review"[T]he book is a valuable and important addition to libraries, personal and institutional. It would serve as an excellent textbook to students taking up research in elementary particle physics and also as a reference volume."--B. Ananthanarayan, Current Science
£70.40
Princeton University Press Quantum Mechanics in a Nutshell
Book SynopsisEmphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, this book proceeds from solving for the properties of a single particle in potential; to solving for two particles (the helium atom); to addressing many-particle systems.Trade Review"Praises in no way can do full justice to the strength and detail of Mahan's well crafted and superb nutshell book. I found the book fascinating, stimulating and convincing and one can easily observe that the book is bursting with intellectual energy and ambition. I am not a rated scientist but as a student and follower of science and scientific projects since the beginning of my academic career, I have come across several books of topical interest but this time I enjoyed Quantum Mechanics in A Nutshell as a whole for its intelligence and manner of treatment of topics. All said and done, it is a book that can be enjoyed by any science student interested in quantum mechanics."--Uwe C. Tauber, Current Engineering Practice "[A] comprehensive and up-to-date exploration of quantum mechanics."--Nature Physics "This book, in spite of 11 chapters densely written, consists of a quick and very readable presentation of basic principles and an impressive number of applications of quantum mechanics. It can be profitably used in courses for beginning, intermediate and, in some cases, advanced students of physics."--Valter Moretti, Zentralblatt MATHTable of ContentsPreface xi Chapter 1: Introduction 1 1.1 Introduction 1 1.2 Schrodinger's Equation 2 1.3 Eigenfunctions 4 1.4 Measurement 8 1.5 Representations 8 1.5.1 Schrodinger Representation 9 1.5.2 Heisenberg Representation 10 1.6 Noncommuting Operators 11 Chapter 2: One Dimension 14 2.1 Square Well 14 2.2 Linear Potentials 26 2.3 Harmonic Oscillator 29 2.4 Raising and Lowering Operators 34 2.5 Exponential Potential 39 2.5.1 Bound State 40 2.5.2 Continuum State 42 2.6 Delta-Function Potential 45 2.7 Number of Solutions 48 2.8 Normalization 49 2.8.1 Bound States 49 2.8.2 Box Normalization 50 2.8.3 Delta-Function Normalization 51 2.8.4 The Limit of Infinite Volume 54 2.9 Wave Packets 56 Chapter 3: Approximate Methods 62 3.1 WKBJ 62 3.2 Bound States by WKBJ 68 3.2.1 Harmonic Oscillator 71 3.2.2 Morse Potential 71 3.2.3 Symmetric Ramp 73 3.2.4 Discontinuous Potentials 74 3.3 Electron Tunneling 76 3.4 Variational Theory 77 3.4.1 Half-Space Potential 80 3.4.2 Harmonic Oscillator in One Dimension 82 Chapter 4: Spin and Angular Momentum 87 4.1 Operators, Eigenvalues, and Eigenfunctions 87 4.1.1 Commutation Relations 88 4.1.2 Raising and Lowering Operators 89 4.1.3 Eigenfunctions and Eigenvalues 90 4.2 Representations 95 4.3 Rigid Rotations 100 4.4 The Addition of Angular Momentum 102 Chapter 5: Two and Three Dimensions 108 5.1 Plane Waves in Three Dimensions 108 5.2 Plane Waves in Two Dimensions 112 5.3 Central Potentials 114 5.3.1 Central Potentials in 3D 114 5.3.2 Central Potential in 2D 118 5.4 Coulomb Potentials 119 5.4.1 Bound States 119 5.4.2 Confluent Hypergeometric Functions 121 5.4.3 Hydrogen Eigenfunctions 121 5.4.4 Continuum States 125 5.5 WKBJ 126 5.5.1 Three Dimensions 126 5.5.2 3D Hydrogen Atom 127 5.5.3 Two Dimensions 128 5.6 Hydrogen-like Atoms 130 5.6.1 Quantum Defect 131 5.6.2 WKBJ Derivation 132 5.6.3 Expectation Values 134 5.7 Variational Theory 134 5.7.1 Hydrogen Atom: n 1 135 5.7.2 Hydrogen Atom: l 1 136 5.7.3 Helium Atom 137 5.8 Free Particles in a Magnetic Field 143 5.8.1 Gauges 143 5.8.2 Eigenfunctions and Eigenvalues 144 5.8.3 Density of States 146 5.8.4 Quantum Hall Effect 147 5.8.5 Flux Quantization 150 Chapter 6: Matrix Methods and Perturbation Theory 157 6.1 H and H0 157 6.2 Matrix Methods 158 6.2.1 2 x 2 160 6.2.2 Coupled Spins 160 6.2.3 Tight-Binding Model 163 6.3 The Stark Effect 166 6.4 Perturbation Theory 170 6.4.1 General Formulas 170 6.4.2 Harmonic Oscillator in Electric Field 174 6.4.3 Continuum States 176 6.4.4 Green's Function 180 6.5 The Polarizability 181 6.5.1 Quantum Definition 182 6.5.2 Polarizability of Hydrogen 183 6.6 Van der Waals Potential 188 6.7 Spin-Orbit Interaction 194 6.7.1 Spin-Orbit in Atoms 195 6.7.2 Alkali Valence Electron in Electric Field 199 6.8 Bound Particles in Magnetic Fields 202 6.8.1 Magnetic Susceptibility 204 6.8.2 Alkali Atom in Magnetic Field 205 6.8.3 Zeeman Effect 207 6.8.4 Paschen-Back Effect 209 Chapter 7: Time-Dependent Perturbations 213 7.1 Time-Dependent Hamiltonians 213 7.2 Sudden Approximation 215 7.2.1 Shake-up and Shake-off 216 7.2.2 Spin Precession 218 7.3 Adiabatic Approximation 220 7.4 Transition Rates: The Golden Rule 222 7.5 Atomic Excitation by a Charged Particle 226 7.6 Born Approximation to Scattering 231 7.6.1 Cross Section 232 7.6.2 Rutherford Scattering 235 7.6.3 Electron Scattering from Hydrogen 236 7.7 Particle Decay 237 Chapter 8: Electromagnetic Radiation 244 8.1 Quantization of the Field 245 8.1.1 Gauges 246 8.1.2 Lagrangian 250 8.1.3 Hamiltonian 253 8.1.4 Casimir Force 256 8.2 Optical Absorption by a Gas 258 8.2.1 Entangled Photons 268 8.3 Oscillator Strength 269 8.4 Polarizability 273 8.5 Rayleigh and Raman Scattering 278 8.6 Compton Scattering 283 Chapter 9: Many-Particle Systems 288 9.1 Introduction 288 9.2 Fermions and Bosons 289 9.2.1 Two Identical Particles 290 9.3 Exchange Energy 291 9.3.1 Two-Electron Systems 291 9.3.2 Parahelium and Orthohelium 293 9.3.3 Hund's Rules 293 9.4 Many-Electron Systems 295 9.4.1 Evaluating Determinants 295 9.4.2 Ground-State Energy 297 9.4.3 Hartree-Fock Equations 299 9.4.4 Free Electrons 301 9.4.5 Pair Distribution Function 303 9.4.6 Correlation Energy 304 9.4.7 Thomas-Fermi Theory 304 9.4.8 Density Functional Theory 307 9.5 Second Quantization 309 9.5.1 Bosons 309 9.5.2 Fermions 312 9.6 Bose-Einstein Condensation 313 9.6.1 Noninteracting Particles 313 9.6.2 Off-Diagonal Long-Range Order 314 Chapter 10: Scattering Theory 320 10.1 Elastic Scattering 320 10.1.1 Partial Wave Analysis 323 10.1.2 Scattering in Two Dimensions 326 10.1.3 Hard-Sphere Scattering 328 10.1.4 Ramsauer-Townsend Effect 330 10.1.5 Born Approximation 332 10.2 Scattering of Identical Particles 333 10.2.1 Two Free Particles 333 10.2.2 Electron Scattering from Hydrogen 335 10.3 T-Matrices 337 10.4 Distorted Wave Scattering 340 10.5 Scattering from Many Particles 343 10.5.1 Bragg Scattering 343 10.5.2 Scattering by Fluids 344 10.5.3 Strong Scattering 346 10.6 Wave Packets 347 10.6.1 Three Dimensions 347 10.6.2 Scattering by Wave Packets 348 Chapter 11: Relativistic Quantum Mechanics 352 11.1 Four-Vectors 352 11.2 Klein-Gordon Equation 354 11.2.1 Derivation 354 11.2.2 Free Particle 354 11.2.3 Currents and Densities 355 11.2.4 Step Potential 356 11.2.5 Nonrelativistic Limit 356 11.2.6 -Mesonic Atoms 357 11.3 Dirac Equation 360 11.3.1 Derivation 361 11.3.2 Current and Charge Density 364 11.3.3 Gamma-Matrices 364 11.3.4 Free-Particle Solutions 366 11.3.5 Spin-Projection Operators 369 11.3.6 Scattering of Dirac Particles 371 11.4 Antiparticles and Negative Energy States 374 11.5 Spin Averages 377 11.6 Nonrelativistic Limit 379 11.6.1 First Approximation 379 11.6.2 Second Approximation 380 11.6.3 Relativistic Corrections for Hydrogenic States 382 11.7 Relativistic Interactions 384 11.7.1 Photon Green's Function 384 11.7.2 Electron Green's Function 387 11.7.3 Boson Exchange 387 11.8 Scattering of Electron and Muon 388 Index 397
£73.60
Princeton University Press Principles of Laser Spectroscopy and Quantum
Book SynopsisSuitable for graduate students studying the interaction of optical fields with atoms, this book provides an introduction to the prototypical problems of radiation fields interacting with two- and three- level atomic systems.Trade Review"Berman and Malinovsky's book can be recommended to graduate students and workers transferring from other areas."--D.G.C. Jones, Contemporary Physics "This high-quality, well-written book is a fine addition to the literature of modern optics... The general style is lucid and entirely fitting for a textbook... In all, this is a splendid book and I am confident that it will be widely received with considerable enthusiasm."--David L. Andrews, Optics & Photonics NewsTable of ContentsPreface xv Chapter 1: Preliminaries 1 Chapter 2: Two-Level Quantum Systems 17 Chapter 3: Density Matrix for a Single Atom 56 Chapter 4: Applications of the Density Matrix Formalism 83 Chapter 5: Density Matrix Equations: Atomic Center-of-Mass Motion, Elementary Atom Optics, and Laser Cooling 99 Chapter 6: Maxwell-Bloch Equations 120 Chapter 7: Two-Level Atoms in Two or More Fields: Introduction to Saturation Spectroscopy 136 Chapter 8: Three-Level Atoms: Applications to Nonlinear Spectroscopy-Open Quantum Systems 159 Chapter 9: Three-Level Atoms: Dark States, Adiabatic Following, and Slow Light 184 Chapter 10: Coherent Transients 206 Chapter 11: Atom Optics and Atom Interferometry 242 Chapter 12: The Quantized, Free Radiation Field 280 Chapter 13: Coherence Properties of the Electric Field 312 Chapter 14: Photon Counting and Interferometry 339 Chapter 15: Atom-Quantized Field Interactions 358 Chapter 17: Optical Pumping and Optical Lattices 402 Chapter 18: Sub-Doppler Laser Cooling 422 Chapter 19: Operator Approach to Atom-Field Interactions: Source-Field Equation 453 Chapter 20: Light Scattering 474 Chapter 21: Entanglement and Spin Squeezing 492 References 506 Bibliography 507 Index 509
£87.20
Princeton University Press Can the Laws of Physics Be Unified
Book SynopsisTrade Review"This book is a very worthwhile, balanced, and useful summary of our current understanding of the fundamental laws of physics. Langacker covers a large amount of material in a very digestible way."—Savdeep Sethi, University of Chicago"Langacker is a renowned expert in particle physics who has made fundamental contributions to the field and lived through the golden era of the standard model. Not surprisingly, the scientific level of this informative book is impeccable."—Gian Francesco Giudice, author of A Zeptospace Odyssey: A Journey into the Physics of the LHC"Langacker has written a useful and informative book that brings the standard model to a broad audience of scientists and aspiring scientists who are interested in the current status of particle physics."—Tom Lubensky, University of PennsylvaniaTable of ContentsPreface vii 1. The Epic Quest 1 2 The Three Eras 7 2.1 The Ingredients 7 2.2 Prehistory 9 2.3 The Era of Exploration 12 2.4 The Standard Model Era 22 2.5 Beyond the Standard Model 26 3 Particles, Interactions, and Cosmology 29 3.1 The Fundamental Particles 29 3.2 The Interactions 35 3.3 Cosmology 41 4 The Standard Model 51 4.1 Gauge Invariance and QED 51 4.2 Internal Symmetries 65 4.3 Yang-Mills Theories 70 4.4 Quantum Chromodynamics 73 4.5 The SU(2) x U(1) Model 83 4.6 The Higgs Mechanism 86 4.7 The Electroweak Theory 91 5 What Don't We Know? 137 5.1 Arbitrariness and Tuning 138 5.2 Terra Incognita: Unanswered Questions 151 5.3 Are the Paradigms Correct? 163 6 How Will We Find Out? 175 6.1 The Ideas 175 6.2 The Tests 211 7. Epilogue: The Dream 223 Postscript: Run 2 226 Glossary 229 Bibliography 251 Index 259
£31.50
Princeton University Press Einstein and the Quantum
Book SynopsisEinstein and the Quantum reveals for the first time the full significance of Albert Einstein's contributions to quantum theory. Einstein famously rejected quantum mechanics, observing that God does not play dice. But, in fact, he thought more about the nature of atoms, molecules, and the emission and absorption of light--the core of what we now knoTrade ReviewWinner of the 2014 Phi Beta Kappa Award in Science, Phi Beta Kappa Society One of Physics World's Top Ten Books of the Year for 2014 One of Choice's Outstanding Academic Titles for 2014 One of Scientific American's Best 2013 Books for the Physics Fan, chosen by Jennifer Ouellette One of Science Friday's Science Book Picks for 2013, chosen by Ira Flatow One of nbc.com's "Holiday Gift Books Span the Science Spectrum" for 2014 "Brief, pacey and lucid... The breadth and depth of Einstein's contribution in this area becomes overwhelmingly clear... Worth a read because it demonstrates that there is more to Einstein's oeuvre than even most quantum physicists know. Stone concludes that Einstein's work was worthy of four Nobel prizes, and it is a measure of the book's achievement that his claim sounds quite reasonable."--Graham Farmelo, Nature "Albert Einstein (1879-1955) is as famous for his paradigm-shifting theories of relativity as he is for his grudge against quantum mechanics, but Stone's (Physics/Yale Univ.) engaging history of Einstein's ardent search for a unifying theory tells a different story. Einstein's creative mind was behind almost every single major development in quantum mechanics... The author adeptly weaves his subject's personal life and scientific fame through the tumult of world war and, in accessible and bright language, brings readers deep into Einstein's struggle with both the macroscopic reality around him and the quantum reality he was trying to unlock... A wonderful reminder that Einstein's monumental role in the development of contemporary science is even more profound than history has allowed."--Kirkus Reviews "A fascinating book, so well written lay people can easily understand this. It is full of science and personality."--Ira Flatow, Science Friday, NPR "In Einstein and the Quantum: The Quest of the Valiant Swabian (Princeton University Press), a historical analysis leavened by many personal stories about Albert Einstein, A. Douglas Stone argues persuasively and engagingly that although this iconic scientist rejected quantum theory as a final theory of microscopic physics, he was responsible for most of its central concepts, including wave-particle duality, indeterminacy and the implications of identicalness."--Sir Michael Berry, Times Higher Education "Professor Douglas Stone has written an engaging book about Einstein's contributions to early quantum theory. He makes a convincing case that these contributions, most of which were made in the 20 year period between 1905 and 1925, have been historically undervalued and that it was Einstein himself, not Planck or Bohr, who deserves most credit for the initial development of quantum theory... Excellent."--Paul Edwards, Australian Physics "This is an excellent book that I recommend without reservation... Any academic library should acquire this book as should any medium-to-large public library system. It would also make a wonderful gift for the physics or science fan in your life."--John Dupuis, Confessions of a Science Librarian "In consummate detail and with a flair for the written word, [Stone] delves into Einstein's original rationale for espousing the quantum, his use of it to account for the mysterious behavior of specific heats at low temperatures, his explanations of spontaneous and stimulated emissions, and the derivation of the statistics of integer-spin particles. Readers benefit from Stone's deep understanding of quantum physics as well as his thoroughness in citing primary Einstein documents--rather than regurgitating the opinions of others--to support his conclusions... There are only a few books on the history of physics that I can heartily recommend to both scholarly historians and physicists interested in the history of their discipline. Because of Stone's extensive research and writing abilities, Einstein and the Quantum is indeed one of those books."--Michael Riordan, Forum on the History of Physics "Einstein and the Quantum is delightful to read, with numerous historical details that were new to me and cham1ing vignettes of Einstein and his colleagues. By avoiding mathematics, Stone makes his book accessible to general readers, but even physicists who are well versed in Einstein and his physics are likely to find new insights into the most remarkable mind of the modern era."--Daniel Kleppner, Physics Today "This engaging book shows that Einstein spent more of his career on quantum physics than on relativity theory and was deeply involved in discussions that shaped current understanding of the subject... His well-written book makes often-trod history fresh, with new perspectives and unfamiliar quotations from Einstein and his peers. Anyone with an interest in the subject, from scholars to laypersons, can read and enjoy this book."--Choice "The book is probably best suited to readers who are already familiar with the basic principles of late classical and early quantum physics. However, in many cases, Stone's explanations are better and more intuitive than those found in traditional textbooks; for this reason, Einstein and the Quantum would make excellent 'further reading' for undergraduate courses in thermodynamics, modern physics or the history of science. Stone also has a knack for summing up complex ideas in a way that even novices will understand."--Physics World "A five star, standout book... If you really want a feel for where quantum physics came from ... it is well worth it."--Popular Science (U.K.) "Stone is a talented writer. Employing a sharp, clean and ironic prose, he translates into intuitive images and limpid reasoning a set of complex physics arguments, which might appear at first sight incomprehensible without a clear understanding of the technical terms. It is remarkable that the author manages to do this by employing just a handful of elementary equations. Even the uninitiated reader can grasp the essential features of Einstein's groundbreaking proposals as well as of the theoretical problems he was facing. In my opinion, this is the major strength of Stone's book, which makes it much more accessible than other scholarly works that present Einstein's involvement in the development of quantum theory in a more technical fashion."--Roberto Lalli, Metascience "[S]ome background knowledge in physics is required in order to understand the discipline-specific terminology and to fully appreciate the depth of Stone's elaborations. Having said that, even specialized physicists will not be disappointed by the author's scholarly efforts."--Christopher B. Germann, Leonardo Reviews "This excellent book can be best recommended to everybody interested is the early history of quantum theory and the impact of A. Einstein."--K. E. Hellwig, Zentralblatt MATHTable of ContentsPreface to the Paperback Edition ix Acknowledgments ix Introduction A Hundred Times More Than Relativity Theory 1 Chapter 1 "An Act of Desperation" 5 Chapter 2 The Impudent Swabian 15 Chapter 3 The Gypsy Life 21 Chapter 4 Two Pillars of Wisdom 26 Chapter 5 The Perfect Instruments of the Creator 36 Chapter 6 More Heat Than Light 44 Chapter 7 Difficult Counting 51 Chapter 8 Those Fabulous Molecules 62 Chapter 9 Tripping the Light Heuristic 70 Chapter 10 Entertaining the Contradiction 80 Chapter 11 Stalking the Planck 86 Chapter 12 Calamity Jeans 94 Chapter 13 Frozen Vibrations 103 Chapter 14 Planck's Nobel Nightmare 111 Chapter 15 Joining the Union 122 Chapter 16 Creative Fusion 129 Chapter 17 The Importance of Being Nernst 141 Chapter 18 Lamenting the Ruins 149 Chapter 19 A Cosmic Interlude 160 Chapter 20 Bohr's Atomic Sonata 168 Chapter 21 Relying on Chance 181 Chapter 22 Chaotic Ghosts 193 Chapter 23 Fifteen Million Minutes of Fame 204 Chapter 24 The Indian Comet 215 Chapter 25 Quantum Dice 228 Chapter 26 The Royal Marriage: E = mc2 = hnu 241 Chapter 27 The Viennese Polymath 254 Chapter 28 Confusion and Then Uncertainty 268 Chapter 29 Nicht diese Tone 279 Appendix 1: The Physicists 287 Appendix 2: The Three Thermal Radiation Laws 291 Notes 295 References 319 Index 325
£17.09
Princeton University Press Group Theory
Book SynopsisTrade Review"This book has to be seen to be believed! The title, Group Theory, is nothing if not surprising, given that the material dealt with by Predrag Cvitanović in these roughly 250 pages requires a level of sophistication well beyond what is offered in the early stages of university algebra. In point of fact, the general theme of the book under review is Lie theory with representation theory in the foreground, and Cvitanović's revolutionary goal (e.g., 'birdtracks') and, for lack of a better word, the attendant combinatorics. . . . [F]or the right reader, which is to say, an R>0-linear combination of mathematician and physicist equipped with a zeal for novel combinatorics flavored diagram-gymnastics, this book will be a treat and a thrill, and its new and radical way to compute many things Lie is bound to make its mark."---Michael Berg, MAA Reviews"More than just an innovative notation, this book offers a conceptually novel alternative path to a key mathematical result, the classification of finite-dimensional simple Lie algebras. . . . While this volume is an obvious resource for physics students, the traces of physics that remain in the work will elucidate for mathematics students how physics uses Lie groups as a tool."---D.V. Feldman, Choice"I think that the book is a very interesting and thought provoking contribution to the literature on representations of compact Lie groups. It has many interesting original aspects that deserve to be known much better than they are."---Karl-Hermann Neeb, Journal of the Lie Theory"[T]he narrative of the book is written in a relaxed and witty style. The book is intriguing as well as entertaining."---Jeb F. Willenbring, Mathematical Reviews
£46.75
MP-AMM American Mathematical Classical and Quantum Computation
Book SynopsisPresents an introduction to the theory of quantum computing. This book starts with the basics of classical theory of computation: Turing machines, Boolean circuits, parallel algorithms, probabilistic computation, NP-complete problems, and the idea of complexity of an algorithm. It provides an exposition of quantum computation theory.Table of ContentsIntroduction Classical computation Quantum computation Solutions Elementary number theory Bibliography Index.
£64.80
MP-AMM American Mathematical Functional Integration and Quantum Physics
Book SynopsisFocuses on probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), this book presents four different proofs of the Feynman-Kac formula.Table of ContentsIntroduction The basic processes Bound state problems Inequalities Magnetic fields and stochastic integrals Asymptotics Other topics References Index Bibliographic supplement Bibliography.
£46.95
MP-AMM American Mathematical Applied Asymptotic Analysis
Book SynopsisA survey of asymptotic methods set in the applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. It is suitable for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering.Table of ContentsFundamentals: Themes of asymptotic analysis The nature of asymptotic approximations Asymptotic analysis of exponential integrals: Fundamental techniques for integrals Laplace's method for asymptotic expansions of integrals The method of steepest descents for asymptotic expansions of integrals The method of stationary phase for asymptotic analysis of oscillatory integrals Asymptotic analysis of differential equations: Asymptotic behavior of solutions of linear second-order differential equations in the complex plane Introduction to asymptotics of solutions of ordinary differential equations with respect to parameters Asymptotics of linear boundary-value problems Asymptotics of oscillatory phenomena Weakly nonlinear waves Appendix: Fundamental inequalities Bibliography Index of names Subject index.
£106.20
MP-AMM American Mathematical Yangians and Classical Lie Algebras
Book SynopsisThe Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St Petersburg's school of mathematical physics in the 1980s. The book gives an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.Table of ContentsYangian for $\mathfrak{g1}_N$ Twisted Yangians Irreducible representations of Y ($\mathfrak{g1}_N$) Irreducible representations of Y($\mathfrak{g}_N$) Gelfand-Tsetlin bases for representations of Y($\mathfrak{g1}_N$) Tensor products of evaluation modules for Y($\mathfrak{g1}_N$) Casimir elements and Capelli identities Centralizer construction Weight bases for representations of $\mathfrak{g}_N$ Bibliography Index.
£103.50
John Wiley & Sons Inc Advanced Quantum Communications
Book SynopsisThe book provides an overview of the most advanced quantum informational geometric techniques, which can help quantum communication theorists analyze quantum channels, such as security or additivity properties. Each section addresses an area of major research of quantum information theory and quantum communication networks. The authors present the fundamental theoretical results of quantum information theory, while also presenting the details of advanced quantum ccommunication protocols with clear mathematical and information theoretical background. This book bridges the gap between quantum physics, quantum information theory, and practical engineering.Table of ContentsPREFACE xvii CHAPTER 1 INTRODUCTION 1 1.1 Emerging Quantum Infl uences 2 1.2 Quantum Information Theory 2 1.3 Different Capacities of Quantum Channels 3 1.4 Challenges Related to Quantum Channel Capacities 5 1.5 Secret and Private Quantum Communication 6 1.6 Quantum Communications Networks 8 1.7 Recent Developments and Future Directions 9 CHAPTER 2 INTRODUCTION TO QUANTUM INFORMATION THEORY 11 2.1 Introduction 12 2.2 Basic Definitions and Formulas 15 2.3 Geometrical Interpretation of the Density Matrices 25 2.4 Quantum Entanglement 31 2.5 Entropy of Quantum States 34 2.6 Measurement of the Amount of Entanglement 43 2.7 Encoding Classical Information to Quantum States 49 2.8 Quantum Noiseless Channel Coding 54 2.9 Brief Summary 57 2.10 Further Reading 57 CHAPTER 3 THE CLASSICAL CAPACITIES OF QUANTUM CHANNELS 65 3.1 Introduction 65 3.2 From Classical to Quantum Communication Channels 73 3.3 Transmission of Classical Information over Quantum Channels 77 3.4 The Holevo-Schumacher-Westmoreland Theorem 84 3.5 Classical Communication over Quantum Channels 89 3.6 Brief Summary of Classical Capacities 98 3.7 Multilevel Quantum Systems and Qudit Channels 98 3.8 The Zero-Error Capacity of a Quantum Channel 100 3.9 Further Reading 117 CHAPTER 4 THE QUANTUM CAPACITY OF QUANTUM CHANNELS 126 4.1 Introduction 126 4.2 Transmission of Quantum Information 128 4.3 Quantum Coherent Information 136 4.4 The Asymptotic Quantum Capacity 146 4.5 Relation between Classical and Quantum Capacities of Quantum Channels 149 4.6 Further Reading 151 CHAPTER 5 GEOMETRIC INTERPRETATION OF QUANTUM CHANNELS 156 5.1 Introduction 156 5.2 Geometric Interpretation of the Quantum Channels 157 5.3 Geometric Interpretation of the Quantum Informational Distance 162 5.4 Computation of Smallest Quantum Ball to Derive the HSW Capacity 182 5.5 Illustrative Example 190 5.6 Geometry of Basic Quantum Channel Models 191 5.7 Geometric Interpretation of HSW Capacities of Different Quantum Channel Models 197 5.8 Further Reading 213 CHAPTER 6 ADDITIVITY OF QUANTUM CHANNEL CAPACITIES 218 6.1 Introduction 218 6.2 Additivity of Classical Capacity 223 6.3 Additivity of Quantum Capacity 225 6.4 Additivity of Holevo Information 232 6.5 Geometric Interpretation of Additivity of HSW Capacity 245 6.6 Classical and Quantum Capacities of some Channels 260 6.7 The Classical Zero-Error Capacities of some Quantum Channels 264 6.8 Further Reading 265 CHAPTER 7 SUPERACTIVATION OF QUANTUM CHANNELS 269 7.1 Introduction 270 7.2 The Non-Additivity of Private Information 270 7.3 Channel Combination for Superadditivity of Private Information 274 7.4 Superactivation of Quantum Capacity of Zero-Capacity Quantum Channels 282 7.5 Behind Superactivation: The Information Theoretic Description 295 7.6 Geometrical Interpretation of Quantum Capacity 302 7.7 Example of Geometric Interpretation of Superactivation 305 7.8 Extension of Superactivation for More General Classes 310 7.9 Superactivation of Zero-Error Capacities 315 7.10 Further Reading 322 CHAPTER 8 QUANTUM SECURITY AND PRIVACY 325 8.1 Introduction 326 8.2 Quantum Key Distribution 330 8.3 Private Communication over the Quantum Channel 333 8.4 Quantum Cryptographic Primitives 336 8.5 Further Reading 354 CHAPTER 9 QUANTUM COMMUNICATION NETWORKS 362 9.1 Long-Distance Quantum Communications 362 9.2 Levels of Entanglement Swapping 368 9.3 Scheduling Techniques of Purifi cation 371 9.4 Hybrid Quantum Repeater 375 9.5 Probabilistic Quantum Networks 382 9.6 Conclusions 384 9.7 Further Reading 384 CHAPTER 10 RECENT DEVELOPMENTS AND FUTURE DIRECTIONS 388 10.1 Introduction 388 10.2 Qubit Implementations 391 10.3 Quantum CPUs 396 10.4 Quantum Memories 400 10.5 Further Reading 411 NOTATIONS AND ABBREVIATIONS 413 REFERENCES 420 INDEX 455
£117.85
John Wiley & Sons Inc Control of Quantum Systems
Book SynopsisAdvanced research reference examining the closed and open quantum systems Control of Quantum Systems: Theory and Methods provides an insight into the modern approaches to control of quantum systems evolution, with a focus on both closed and open (dissipative) quantum systems.Table of ContentsAbout the Author xiii Preface xv 1 Introduction 1 1.1 Quantum States 2 1.2 Quantum Systems Control Models 3 1.2.1 Schrödinger Equation 4 1.2.2 Liouville Equation 4 1.2.3 Markovian Master Equations 5 1.2.4 Non-Markovian Master Equations 5 1.3 Structures of Quantum Control Systems 6 1.4 Control Tasks and Objectives 8 1.5 System Characteristics Analyses 9 1.5.1 Controllability 9 1.5.2 Reachability 9 1.5.3 Observability 10 1.5.4 Stability 10 1.5.5 Convergence 10 1.5.6 Robustness 10 1.6 Performance of Control Systems 11 1.6.1 Probability 11 1.6.2 Fidelity 11 1.6.3 Purity 12 1.7 Quantum Systems Control 13 1.7.1 Description of Control Problems 13 1.7.2 Quantum Control Theory and Methods 13 1.8 Overview of the Book 16 References 18 2 State Transfer and Analysis of Quantum Systems on the Bloch Sphere 21 2.1 Analysis of a Two-level Quantum System State 21 2.1.1 Pure State Expression on the Bloch Sphere 21 2.1.2 Mixed States in the Bloch Sphere 24 2.1.3 Control Trajectory on the Bloch Sphere 26 2.2 State Transfer of Quantum Systems on the Bloch Sphere 27 2.2.1 Control of a Single Spin-1/2 Particle 28 2.2.2 Situation with the Minimum Ωt of Control Fields 30 2.2.3 Situation with a Fixed Time T 31 2.2.4 Numerical Simulations and Results Analyses 33 References 37 3 Control Methods of Closed Quantum Systems 39 3.1 Improved Optimal Control Strategies Applied in Quantum Systems 39 3.1.1 Optimal Control of Quantum Systems 40 3.1.2 Improved Quantum Optimal Control Method 42 3.1.3 Krotov-Based Method of Optimal Control 43 3.1.4 Numerical Simulation and Performance Analysis 45 3.2 Control Design of High-Dimensional Spin-1/2 Quantum Systems 48 3.2.1 Coherent Population Transfer Approaches 48 3.2.2 Relationships between the Hamiltonian of Spin-1/2 Quantum Systems under Control and the Sequence of Pulses 49 3.2.3 Design of the Control Sequence of Pulses 52 3.2.4 Simulation Experiments of Population Transfer 53 3.3 Comparison of Time Optimal Control for Two-Level Quantum Systems 57 3.3.1 Description of System Model 58 3.3.2 Geometric Control 59 3.3.3 Bang-Bang Control 61 3.3.4 Time Comparisons of Two Control Strategies 64 3.3.5 Numerical Simulation Experiments and Results Analyses 66 References 71 4 Manipulation of Eigenstates – Based on Lyapunov Method 73 4.1 Principle of the Lyapunov Stability Theorem 74 4.2 Quantum Control Strategy Based on State Distance 75 4.2.1 Selection of the Lyapunov Function 76 4.2.2 Design of the Feedback Control Law 77 4.2.3 Analysis and Proof of the Stability 78 4.2.4 Application to a Spin-1/2 Particle System 80 4.3 Optimal Quantum Control Based on the Lyapunov Stability Theorem 81 4.3.1 Description of the System Model 82 4.3.2 Optimal Control Law Design and Property Analysis 84 4.3.3 Simulation Experiments and the Results Comparisons 86 4.4 Realization of the Quantum Hadamard Gate Based on the Lyapunov Method 88 4.4.1 Mathematical Model 89 4.4.2 Realization of the Quantum Hadamard Gate 90 4.4.3 Design of Control Fields 92 4.4.4 Numerical Simulations and Comparison Results Analyses 94 References 96 5 Population Control Based on the Lyapunov Method 99 5.1 Population Control of Equilibrium State 99 5.1.1 Preliminary Notions 99 5.1.2 Control Laws Design 100 5.1.3 Analysis of the Largest Invariant Set 101 5.1.4 Considerations on the Determination of P 104 5.1.5 Illustrative Example 105 5.1.6 Appendix: Proof of Theorem 5.1 107 5.2 Generalized Control of Quantum Systems in the Frame of Vector Treatment 110 5.2.1 Design of Control Law 110 5.2.2 Convergence Analysis 113 5.2.3 Numerical Simulation on a Spin-1/2 System 114 5.3 Population Control of Eigenstates 117 5.3.1 System Model and Control Laws 117 5.3.2 Largest Invariant Set of Control Systems 118 5.3.3 Analysis of the Eigenstate Control 118 5.3.4 Simulation Experiments 119 References 123 6 Quantum General State Control Based on Lyapunov Method 125 6.1 Pure State Manipulation 125 6.1.1 Design of Control Law and Discussion 125 6.1.2 Control System Simulations and Results Analyses 129 6.2 Optimal Control Strategy of the Superposition State 131 6.2.1 Preliminary Knowledge 132 6.2.2 Control Law Design 133 6.2.3 Numerical Simulations 134 6.3 Optimal Control of Mixed-State Quantum Systems 135 6.3.1 Model of the System to be Controlled 136 6.3.2 Control Law Design 137 6.3.3 Numerical Simulations and Results Analyses 142 6.4 Arbitrary Pure State to a Mixed-State Manipulation 145 6.4.1 Transfer from an Arbitrary Pure State to an Eigenstate 146 6.4.2 Transfer from an Eigenstate to a Mixed State by Interaction Control 147 6.4.3 Control Design for a Mixed-State Transfer 149 6.4.4 Numerical Simulation Experiments 151 References 154 7 Convergence Analysis Based on the Lyapunov Stability Theorem 155 7.1 Population Control of Quantum States Based on Invariant Subsets with the Diagonal Lyapunov Function 155 7.1.1 System Model and Control Design 155 7.1.2 Correspondence between any Target Eigenstate and the Value of the Lyapunov Function 156 7.1.3 Invariant Set of Control Systems 157 7.1.4 Numerical Simulations 161 7.1.5 Summary and Discussion 164 7.2 A Convergent Control Strategy of Quantum Systems 165 7.2.1 Problem Description 165 7.2.2 Construction Method of the Observable Operator 166 7.2.3 Proof of Convergence 168 7.2.4 Route Extension Strategy 173 7.2.5 Numerical Simulations 174 7.3 Path Programming Control Strategy of Quantum State Transfer 176 7.3.1 Control Law Design Based on the Lyapunov Method in the Interaction Picture 177 7.3.2 Transition Path Programming Control Strategy 178 7.3.3 Numerical Simulations and Results Analyses 182 References 186 8 Control Theory and Methods in Degenerate Cases 187 8.1 Implicit Lyapunov Control of Multi-Control Hamiltonian Systems Based on State Error 187 8.1.1 Control Design 188 8.1.2 Convergence Proof 192 8.1.3 Relation between Two Lyapunov Functions 193 8.1.4 Numerical Simulation and Result Analysis 193 8.2 Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity 195 8.2.1 Control Law Design and Convergence Proof 195 8.2.2 Numerical Simulation and Result Analysis 199 8.3 Implicit Lyapunov Control for the Quantum Liouville Equation 200 8.3.1 Description of Problem 201 8.3.2 Derivation of Control Laws 202 8.3.3 Convergence Analysis 205 8.3.4 Numerical Simulations 209 References 211 9 Manipulation Methods of the General State 213 9.1 Quantum System Schmidt Decomposition and its Geometric Analysis 213 9.1.1 Schmidt Decomposition of Quantum States 214 9.1.2 Definition of Entanglement Degree Based on the Schmidt Decomposition 215 9.1.3 Application of the Schmidt Decomposition 216 9.2 Preparation of Entanglement States in a Two-Spin System 220 9.2.1 Construction of the Two-Spin Systems Model in the Interaction Picture 220 9.2.2 Design of the Control Field Based on the Lyapunov Method 223 9.2.3 Proof of Convergence for the Bell States 226 9.2.4 Numerical Simulations 227 9.3 Purification of the Mixed State for Two-Dimensional Systems 230 9.3.1 Purification by Means of a Probe 230 9.3.2 Purification by Interaction Control 232 9.3.3 Numerical Experiments and Results Comparisons 233 9.3.4 Discussion 234 References 235 10 State Control of Open Quantum Systems 237 10.1 State Transfer of Open Quantum Systems with a Single Control Field 237 10.1.1 Dynamical Model of Open Quantum Systems 237 10.1.2 Derivation of Optimal Control Law 238 10.1.3 Control System Design 241 10.1.4 Numerical Simulations and Results Analyses 242 10.2 Purity and Coherence Compensation through the Interaction between Particles 246 10.2.1 Method of Compensation for Purity and Coherence 247 10.2.2 Analysis of System Evolution 250 10.2.3 Numerical Simulations 253 10.2.4 Discussion 255 Appendix 10.A Proof of Equation 10.59 257 References 258 11 State Estimation, Measurement, and Control of Quantum Systems 261 11.1 State Estimation Methods in Quantum Systems 261 11.1.1 Background of State Estimation of Quantum Systems 262 11.1.2 Quantum State Estimation Methods Based on the Measurement of Identical Copies 262 11.1.3 Quantum State Reconstruction Methods Based on System Theory 267 11.2 Entanglement Detection and Measurement of Quantum Systems 268 11.2.1 Entanglement States 269 11.2.2 Entanglement Witnesses 271 11.2.3 Entanglement Measures 273 11.2.4 Non-linear Separability Criteria 277 11.3 Decoherence Control Based on Weak Measurement 278 11.3.1 Construction of a Weak Measurement Operator 279 11.3.2 Applicability of Weak Measurement 280 11.3.3 Effects on States 282 Appendix 11.A Proof of Normed Linear Space (A, ¡¬ • ¡¬) 286 References 287 12 State Preservation of Open Quantum Systems 291 12.1 Coherence Preservation in a Λ-Type Three-Level Atom 291 12.1.1 Models and Objectives 292 12.1.2 Design of Control Field 294 12.1.3 Analysis of Singularities Issues 297 12.1.4 Numerical Simulations 299 12.2 Purity Preservation of Quantum Systems by a Resonant Field 301 12.2.1 Problem Description 302 12.2.2 Purity Property Preservation 303 12.2.3 Discussion 306 12.3 Coherence Preservation in Markovian Open Quantum Systems 307 12.3.1 Problem Formulation 308 12.3.2 Design of Control Variables 311 12.3.3 Numerical Simulations 313 12.3.4 Discussion 315 Appendix 12.A Derivation of HC 316 References 317 13 State Manipulation in Decoherence-Free Subspace 321 13.1 State Transfer and Coherence Maintainance Based on DFS for a Four-Level Energy Open Quantum System 321 13.1.1 Construction of DFS and the Desired Target State 322 13.1.2 Design of the Lyapunov-Based Control Law for State Transfer 325 13.1.3 Numerical Simulations 326 13.2 State Transfer Based on a Decoherence-Free Target State for a Λ-Type N-Level Atomic System 328 13.2.1 Construction of the Decoherence-Free Target State 328 13.2.2 Design of the Lyapunov-Based Control Law for State Transfer 331 13.2.3 Numerical Simulations and Results Analyses 332 13.3 Control of Quantum States Based on the Lyapunov Method in Decoherence-Free Subspaces 336 13.3.1 Problem Description 336 13.3.2 Control Design in the Interaction Picture 338 13.3.3 Construction of P and Convergence Analysis 339 13.3.4 Numerical Simulation Examples and Discussion 345 References 348 14 Dynamic Decoupling Quantum Control Methods 351 14.1 Phase Decoherence Suppression of an n-Level Atom in Ξ;-Configuration with Bang-Bang Controls 351 14.1.1 Dynamical Decoupling Mechanism 352 14.1.2 Design of the Bang–Bang Operations Group in Phase Decoherence 355 14.1.3 Examples of Design 357 14.2 Optimized Dynamical Decoupling in Ξ-Type n-Level Atom 360 14.2.1 Periodic Dynamical Decoupling 361 14.2.2 Uhrig Dynamical Decoupling 361 14.2.3 Behaviors of Quantum Coherence under Various Dynamical Decoupling Schemes 362 14.2.4 Examples 365 14.2.5 Discussion 366 14.3 An Optimized Dynamical Decoupling Strategy to Suppress Decoherence 366 14.3.1 Universal Dynamical Decoupling for a Qubit 367 14.3.2 An Optimized Dynamical Decoupling Scheme 369 14.3.3 Simulation and Comparison 369 14.3.4 Discussion 375 References 378 15 Trajectory Tracking of Quantum Systems 381 15.1 Orbit Tracking of Quantum States Based on the Lyapunov Method 382 15.1.1 Description of the System Model 382 15.1.2 Design of Control Law 384 15.1.3 Numerical Simulation Experiments and Results Analysis 385 15.2 Orbit Tracking Control of Quantum Systems 389 15.2.1 System Model and Control Law Design 390 15.2.2 Numerical Simulation Experiments 391 15.3 Adaptive Trajectory Tracking of Quantum Systems 394 15.3.1 Description of the System Model 396 15.3.2 Control System Design and Characteristic Analysis 398 15.3.3 Numerical Simulation and Result Analysis 400 15.4 Convergence of Orbit Tracking for Quantum Systems 402 15.4.1 Description of the Control System Model 403 15.4.2 Control Law Derivation 404 15.4.3 Convergence Analysis 404 15.4.4 Applications and Experimental Results Analyses 411 References 416 Index 419
£114.26
John Wiley & Sons Inc The Pauli Exclusion Principle
Book SynopsisThis is the first scientic book devoted to the Pauli exclusion principle, which is a fundamental principle of quantum mechanics and is permanently applied in chemistry, physics, and molecular biology.Table of ContentsPreface xi 1 Historical Survey 1 1.1 Discovery of the Pauli Exclusion Principle and Early Developments 1 1.2 Further Developments and Still Existing Problems 11 References 21 2 Construction of Functions with a Definite Permutation Symmetry 25 2.1 Identical Particles in Quantum Mechanics and Indistinguishability Principle 25 2.2 Construction of Permutation-Symmetric Functions Using the Young Operators 29 2.3 The Total Wave Functions as a Product of Spatial and Spin Wave Functions 36 2.3.1 Two-Particle System 36 2.3.2 General Case of N-Particle System 41 References 49 3 Can the Pauli Exclusion Principle Be Proved? 50 3.1 Critical Analysis of the Existing Proofs of the Pauli Exclusion Principle 50 3.2 Some Contradictions with the Concept of Particle Identity and their Independence in the Case of the Multidimensional Permutation Representations 56 References 62 4 Classification of the Pauli-Allowed States in Atoms and Molecules 64 4.1 Electrons in a Central Field 64 4.1.1 Equivalent Electrons: L–S Coupling 64 4.1.2 Additional Quantum Numbers: The Seniority Number 71 4.1.3 Equivalent Electrons: j–j Coupling 72 4.2 The Connection between Molecular Terms and Nuclear Spin 74 4.2.1 Classification of Molecular Terms and the Total Nuclear Spin 74 4.2.2 The Determination of the Nuclear Statistical Weights of Spatial States 79 4.3 Determination of Electronic Molecular Multiplets 82 4.3.1 Valence Bond Method 82 4.3.2 Degenerate Orbitals and One Valence Electron on Each Atom 87 4.3.3 Several Electrons Specified on One of the Atoms 91 4.3.4 Diatomic Molecule with Identical Atoms 93 4.3.5 General Case I 98 4.3.6 General Case II 100 References 104 5 Parastatistics, Fractional Statistics, and Statistics of Quasiparticles of Different Kind 106 5.1 Short Account of Parastatistics 106 5.2 Statistics of Quasiparticles in a Periodical Lattice 109 5.2.1 Holes as Collective States 109 5.2.2 Statistics and Some Properties of Holon Gas 111 5.2.3 Statistics of Hole Pairs 117 5.3 Statistics of Cooper’s Pairs 121 5.4 Fractional Statistics 124 5.4.1 Eigenvalues of Angular Momentum in the Three- and Two-Dimensional Space 124 5.4.2 Anyons and Fractional Statistics 128 References 133 Appendix A: Necessary Basic Concepts and Theorems of Group Theory 135 A.1 Properties of Group Operations 135 A.1.1 Group Postulates 135 A.1.2 Examples of Groups 137 A.1.3 Isomorphism and Homomorphism 138 A.1.4 Subgroups and Cosets 139 A.1.5 Conjugate Elements. Classes 140 A.2 Representation of Groups 141 A.2.1 Definition 141 A.2.2 Vector Spaces 142 A.2.3 Reducibility of Representations 145 A.2.4 Properties of Irreducible Representations 147 A.2.5 Characters 148 A.2.6 The Decomposition of a Reducible Representation 149 A.2.7 The Direct Product of Representations 151 A.2.8 Clebsch–Gordan Coefficients 154 A.2.9 The Regular Representation 156 A.2.10 The Construction of Basis Functions for Irreducible Representation 157 References 160 Appendix B: The Permutation Group 161 B.1 General Information 161 B.1.1 Operations with Permutation 161 B.1.2 Classes 164 B.1.3 Young Diagrams and Irreducible Representations 165 B.2 The Standard Young–Yamanouchi Orthogonal Representation 167 B.2.1 Young Tableaux 167 B.2.2 Explicit Determination of the Matrices of the Standard Representation 170 B.2.3 The Conjugate Representation 173 B.2.4 The Construction of an Antisymmetric Function from the Basis Functions for Two Conjugate Representations 175 B.2.5 Young Operators 176 B.2.6 The Construction of Basis Functions for the Standard Representation from a Product of N Orthogonal Functions 178 References 181 Appendix C: The Interconnection between Linear Groups and Permutation Groups 182 C.1 Continuous Groups 182 C.1.1 Definition 182 C.1.2 Examples of Linear Groups 185 C.1.3 Infinitesimal Operators 187 C.2 The Three-Dimensional Rotation Group 189 C.2.1 Rotation Operators and Angular Momentum Operators 189 C.2.2 Irreducible Representations 191 C.2.3 Reduction of the Direct Product of Two Irreducible Representations 194 C.2.4 Reduction of the Direct Product of k Irreducible Representations. 3n − j Symbols 197 C.3 Tensor Representations 201 C.3.1 Construction of a Tensor Representation 201 C.3.2 Reduction of a Tensor Representation into Reducible Components 202 C.3.3 Littlewood’s Theorem 207 C.3.4 The Reduction of U2j + 1 R3 209 C.4 Tables of the Reduction of the Representations U λ 2j+1 to the Group R3 214 References 216 Appendix D: Irreducible Tensor Operators 217 D.1 Definition 217 D.2 The Wigner–Eckart Theorem 220 References 222 Appendix E: Second Quantization 223 References 227 Index 228
£98.06
Springer Relativity in Rotating Frames Relativistic Physics in Rotating Reference Frames Fundamental Theories of Physics 135
Book SynopsisIn order to give the reader a deeper insight into this research field, the contributing authors discuss their opinions on the main subjects in an enthralling virtual round table: in this way, the reader can get a direct comparison of the various viewpoints on the most controversial and interesting topics.Trade ReviewFoundations of Physics, Vol. 34, No. 8, August 2004 (© 2004) Book Review Relativity in Rotating Frames. Relativistic Physics in Rotating Reference Frames. Edited by G.Rizzi and M.L.Ruggiero, (Fundamental Theories of Physics 135), 452 pp., $193.00. ISBN 1-4020-1805-3. Soon after Einstein’s destruction of absolute simultaneity and Minkowski’s formulation of special relativity, the problem of the relativistic description of extended bodies in rotating reference frames led to Ehrenfest’s paradox with the subsequent Einstein’s answer and to an endless still on going debate about the instantaneous space and the geometry of a rotating disk and the associated Sagnac effect. As emphasized by Stachel in the Preface of this book, edited by G.Rizzi and M.L.Ruggiero and composed of invited contributions, from both "traditionalists" and "heretics", the existence of a structural difference between translations and rotations goes back to Aristotle. Only with Newton translations with constant velocity where privileged with respect to other types of motion through the introduction of the notion of inertial reference frame and the law of inertia. This notion survived in Einstein’s formulation of special relativity, but at the price of loosing the concept of instantaneous three-space: only the notion of being space-like with respect to an observer is well de.ned. Since a relativistic, either inertial or no inertial, observer has no "absolute present", the description of extended objects becomes a non-trivial problem. Given only the postulates of special relativity, namely the constancy and isotropy of the round-trip velocity of light involving only one observer and one clock, there is no unique de.nition of synchronization of clocks, of one-way velocity of light and of spatial distance in an instantaneous three-space. We must make some convention, for instance Einstein’s convention of simultaneity in inertial frames implying an isotropic one-way velocity of light and "equal time" hyper-planes, regarding one of these notions to have the other two de.ned. 1281 0015-9018/04/0800-1281/0 © 2004 Plenum Publishing Corporation 1282 Book Review As a consequence, since in non-inertial frames no convention, globally valid like Einstein’s one in inertial frames, is known, different conventions lead to different viewpoints especially in connection with non-inertial uniformly rotating frames and to the necessity of a still lacking interpretation of their equivalence. This so deeply non-Newtonian framework explains why extended objects like the uniformly rotating disk, which presents no conceptual difficulty at the Newtonian level, give rise to a so controversial and non-unique picture at the relativistic level. Grøn’s historical contribution shows how many, often contradictory, viewpoints have been developed in 90 years. This book is really welcome because it gives a snapshot of the existing spectrum of interpretations regarding rotating coordinate systems (Dieks, Bel, Nikolic, de Felice), the locality hypothesis (Mashhoon), inertial forces (Bini, Jantzen), the anisotropy of the velocity of light in rotating frames and the Sagnac effect (Klauber, Selleri, Sera.ni, Rizzi, Ruggiero, Weber, Sorge, Pascual-Sanchez, Vicente), what is the "space of a rotating disk" and how to de.ne length measurements in rotating frames (Rizzi, Ruggiero, Tartaglia, Grøn, Klauber, Nikolic), quantum mechanics in rotating frames and the gravitational .eld (Papini, Anandan, Suzuki). Only Mach’s principle is absent! The absence of agreement among the various interpretations, nicely made explicit through six virtual dialogues at the end of the book, is made more acute by the contributions of Rizzi and Sera.ni on the freedom in the choice of the notion of simultaneity in rotating frames and of Ashby on the relevance of the Sagnac effect in the Global Positioning System especially after the developments of modern technology oriented to space navigation and requiring the synchronization of the now existing ultra-precise atomic clocks till the order 1/c3. In conclusion, it is hoped that this book will be a stimulus to start a fresh search of the missing elements to arrive at a relativistic description of extended objects in arbitrary non-inertial frames. Such a description should include Maxwell equations and should lead to a well-posed Cauchy problem allowing us to get control on the energy balance of every physical system in a non-inertial reference frame. Luca Lusanna Firenze, Italy Table of ContentsI Historical Papers.- 1 Uniform Rotation of Rigid Bodies and the Theory of Relativity.- 2 The existence of the luminiferous ether demonstrated by means of the effect of a relative ether wind in an uniformly rotating interferometer.- II Papers.- 1 The Sagnac Effect in the Global Positioning System.- 2 Space, Time and Coordinates in a Rotating World.- 3 The Hypothesis of Locality and its Limitations.- 4 Sagnac effect: end of the mystery.- 5 Synchronization and desynchronization on rotating platforms.- 6 Toward a Consistent Theory of Relativistic Rotation.- 7 Elementary Considerations of the Time and Geometry of Rotating Reference Frames.- 8 Local and Global Anisotropy in the Speed of Light.- 9 Isotropy of the velocity of light and the Sagnac effect.- 10 The relativistic Sagnac effect: two derivations.- 11 Inertial forces: the special relativistic assessment.- 12 Eppur, si muove!.- 13 Does anything happen on a rotating disk?.- 14 Proper co-ordinates of non-inertial observers and rotation.- 15 Space geometry in rotating reference frames: A historical appraisal.- 16 Quantum Physics in Inertial and Gravitational Fields.- 17 Quantum Mechanics in a Rotating Frame.- 18 On rotating spacetimes.- III Round Table.- I Dialogue on the velocity of light in a rotating frame.- II Dialogue on synchronization and Sagnac effect.- III Dialogue on the measurement of lengths in a rotating frame.- IV Dialogue on the Brillet-Hall experiment.- V Dialogue on quantum effects in rotating systems.- VI Dialogue on non uniform motions and other details about Klauber’s and Selleri’s challenges.
£161.99
Johns Hopkins University Press Wavelets
Book SynopsisNajmi's primer will be an indispensable resource for those in computer science, the physical sciences, applied mathematics, and engineering who wish to obtain an in-depth understanding and working knowledge of this fascinating and evolving field.Trade ReviewA complete, concise and clear exposition of the more traditional tools related to linear filtering. -- Davide Barbieri Mathematical Reviews Since their emergence in the last eighties and early nineties of the twentieth century, wavelets and other multi-scale transforms have become powerful signal and image processing tools. Najmi's book provides physicists and engineers with a clear and concise introduction to this fascinating field. -- Ignace Loris American Journal of PhysicsTable of ContentsList of TablesList of FiguresList of AcronymsPrefaceAcknowledgments1. Analysis in Vector and Function Spaces1.1. Introduction1.2. The Lebesgue Integral1.3. Discrete Time Signals1.4. Vector Spaces1.5. Linear Independence1.6. Bases and Basis Vectors1.7. Normed Vector Spaces1.8. Inner Product1.9. Banach and Hilbert Spaces1.10. Linear Operators, Operator Norm, the Adjoint Operator1.11. Reproducing Kernel Hilbert Space1.12. The Dirac Delta Distribution1.13. Orthonormal Vectors1.14. Orthogonal Projections1.15. Multi-Resolution Analysis Subspaces1.16. Complete and Orthonormal Bases in L2 (R)1.17. The Dirac Notation1.18. The Fourier Transform1.19. The Fourier Series Expansion1.20. The Discrete Time Fourier Transform1.21. The Discrete Fourier Transform1.22. Band-Limited Functions and the Sampling Theorem1.23. The Basis Operator in L2(R)1.24. Biorthogonal Bases and Representations in L2 (R)1.25. Frames in a Finite Dimensional Vector Space1.26. Frames in L2 (R)1.27. Dual Frame Construction Algorithm1.28. Exercises2. Linear Time-Invariant Systems2.1. Introduction2.2. Convolution in Continuous Time2.3. Convolution in Discrete Time2.4. Convolution of Finite Length Sequences2.5. Linear Time-Invariant Systems and the Z Transform2.6. Spectral Factorization for Finite Length Sequences2.7. Perfect Reconstruction Quadrature Mirror Filters2.8. Exercises3. Time, Frequency, and Scale Localizing Transforms3.1. Introduction3.2. The Windowed Fourier Transform3.3. The Windowed Fourier Transform Inverse3.4. The Range Space of the Windowed Fourier Transform3.5. The Discretized Windowed Fourier Transform3.6. Time-Frequency Resolution of theWindowed Fourier Transform3.7. The Continuous Wavelet Transform3.8. The Continuous Wavelet Transform Inverse3.9. The Range Space of the Continuous Wavelet Transform3.10. The Morlet, the Mexican Hat, and the Haar Wavelets3.11. Discretizing the Continuous Wavelet Transform3.12. Algorithm A' Trous3.13. The Morlet Scalogram3.14. Exercises4. The Haar and Shannon Wavelets4.1. Introduction4.2. Haar Multi-Resolution Analysis Subspaces4.3. Summary and Generalization of Results4.4. The Spectra of the Haar Filter Coefficients4.5. Half-Band Finite Impulse Response Filters4.6. The Shannon Scaling Function4.7. The Spectrum of the Shannon Filter Coefficients4.8. Meyer's Wavelet4.9. Exercises5. General Properties of Scaling and Wavelet Functions5.1. Introduction5.2. Multi-Resolution Analysis Spaces5.3. The Inverse Relations5.4. The Shift-Invariant Discrete Wavelet Transform5.5. Time Domain Properties5.6. Examples of Finite Length Filter Coefficients5.7. Frequency Domain Relations5.8. Orthogonalization of a Basis Set: b1 Spline Wavelet5.9. The Cascade Algorithm5.10. Biorthogonal Wavelets5.11. Multi-Resolution Analysis Using Biorthogonal Wavelets5.12. Exercises6. Discrete Wavelet Transform of Discrete Time Signals6.1. Introduction6.2. Discrete Time Data and Scaling Function Expansions6.3. Implementing the DWT for Even Length h0 Filters6.4. Denoising and Thresholding6.5. Biorthogonal Wavelets of Compact Support6.6. The Lazy Filters6.7. Exercises7. Wavelet Regularity and Daubechies Solutions7.1. Introduction7.2. Zero Moments of the Mother Wavelet7.3. The Form of H0(z) and the Decay Rate of F(?)7.4. Daubechies Orthogonal Wavelets of Compact Support7.5. Wavelet and Scaling Function Vanishing Moments7.6. Biorthogonal Wavelets of Compact Support7.7. Biorthogonal Spline Wavelets7.8. The Lifting Scheme7.9. Exercises8. Orthogonal Wavelet Packets8.1. Introduction8.2. Review of the Orthogonal Wavelet Transform8.3. Packet Functions for Orthonormal Wavelets8.4. Discrete Orthogonal Packet Transform of Finite Length Sequences8.5. The Best Basis Algorithm8.6. Exercises9. Wavelet Transform in Two Dimensions9.1. Introduction9.2. The Forward Transform9.3. The Inverse Transform9.4. Implementing the Two-Dimensional Wavelet Transform9.5. Application to Image Compression9.6. Image Fusion9.8. ExercisesBibliographyIndex
£37.35
Springer The Geometry of Spacetime
Book Synopsis1 Relativity Before 1905.- 2 Special Relativity-Kinematics.- 3 Special Relativity-Kinetics.- 4 Arbitrary Frames.- 5 Surfaces and Curvature.- 6 Intrinsic Geometry.- 7 General Relativity.- 8 Consequences.Table of Contents1 Relativity Before 1905.- 2 Special Relativity-Kinematics.- 3 Special Relativity-Kinetics.- 4 Arbitrary Frames.- 5 Surfaces and Curvature.- 6 Intrinsic Geometry.- 7 General Relativity.- 8 Consequences.
£56.24
Society for Industrial & Applied Mathematics,U.S. Formulation and Numerical Solution of Quantum
Book SynopsisThis book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schrödinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose–Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework.This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods.Table of Contents Preface Chapter 1: Introduction Chapter 2: Quantum mechanics and the Schrödinger equation Chapter 3: Optimal control theory for quantum systems Chapter 4: Controllability of quantum systems Chapter 5: Discretization schemes Chapter 6: Numerical optimization methods Chapter 7: Application to quantum control problems Appendix Bibliography Index
£89.25
Toronto Academic Press Quantum Mechanics
£86.40
ISTE Ltd and John Wiley & Sons Inc Time, Emergences and Communications
Book SynopsisThis book presents an attempt to understand emergences in various situations where material components interact by coordinating their actions to "make system" with emerging properties (or functions) accessible to experimental investigation. I will endeavor to show that communications play a decisive role in these processes. A strategy will be implemented. If communications are so important, then we must show that they are an essential property of matter. This justifies the detailed analyses on the quantum world developed in the first five chapters. Also includes a study of the strange property of entanglement as well as an interpretation of the chemical bonds which cannot be circumvented in order to understand the functioning of complex systems; Living cells and animals. So the strategy consolidates as much as possible the physical foundations and the understanding of the primordial matter and then passing to the realities based on very large numbers of elementary components.Table of ContentsIntroduction xi Chapter 1. Quantum Physics and Information 1 1.1. Orthodox introduction to quantum physics 1 1.2. Quantum states or how nature communicates with physicists 6 1.3. Particles, information, evolution 10 1.4. Interpretation of Pauli’s exclusion principle 12 1.5. State vectors, science of orientations 14 1.6. Provisional conclusions on quantum mechanics 18 Chapter 2. Two Quantum Studies 21 2.1. Does the quantum universe observe us? 21 2.2. A detour by statistical mechanics 24 2.3. Expressive and receptive waves in quantum observation 25 2.4. Wave function fission 27 2.5. Form–energy duality in Schrödinger’s equation 29 2.5.1. Separation of spatial and temporal functions 29 2.5.2. Solution to the equation and quantum formalization of the hydrogen atom 31 2.5.3. Form–energy diagram and correspondences 32 2.5.4. Form and content in the quantum atom 33 Chapter 3. Quantum Entanglement 35 3.1. Some considerations on quantum entanglement 35 3.2. The mystery of quantum entanglement 37 3.3. Quantum entanglement and complex sciences: information and system 42 3.4. Concluding remark about strange information 45 Chapter 4. Quantum Darwinism and the Macroscopic World 47 4.1. Quantum Darwinism, from quantum to the observable world 47 4.2. The controversy between W. Zurek and R. Kastner 50 4.3. Understanding our classical perception with quantum physics, an anthropomorphic approach 53 4.4. From quantum substantial matter to spatiotemporal extension 56 Chapter 5. Chemistry and Quantum Communications 59 5.1. Brief epistemological notes 59 5.2. Chemistry, a little-known science that studies bondings and reactions 60 5.3. Orbitals and waves make bonding improbable 64 5.3.1. The electron takes part in the bond, but there is no bond 64 5.3.2. The molecule in question 66 5.4. Quantum bond, orbitals and monadological conception of chemistry 68 5.4.1. The theory of molecular orbitals in chemistry 68 5.4.2. Monadology, bonding and non-bonding orbitals 70 5.5. Molecular quantum communication 72 Chapter 6. Emergences in Matter 75 6.1. Introduction about emergence 75 6.2. The central conjecture in emergence theory 78 6.3. Physics, emergence ontology and communications 80 6.4. Quantum and information in the emergences of condensed matter 83 6.4.1. Material emergences and physical sciences 83 6.4.2. New horizons in the physics of condensed matter 85 6.4.3. Matter and information according to Xiao-Gang Wen 86 6.5. Tensor networks 89 6.5.1. The tools of statistical physics 89 6.5.2. The complicated invisible behind the visible 90 Chapter 7. Communication and Emergence Fields 95 7.1. Communication fields 95 7.1.1. Quantum communications 95 7.1.2. Morphogenetic field or communication field? 97 7.2. Are communication fields structured by quantum matter? 98 7.2.1. The field as a physical concept 98 7.2.2. The Lagrangian and the symmetries, main access door for studying fields as emergences 99 7.3. Is there a relation between quantified fields and emergences? 101 7.4. Brief overview of matter and emergences in contemporary physics 105 7.4.1. Dissipative structures 106 7.4.2. Condensed matter and exotic phases 107 7.4.3. Quantified fields or the emerging “material cosmos” 108 7.4.4. Exotic phases and the model with topology and entanglement 109 7.4.5. Overview, from Plotinus’ two categories of matter to quantum materiality 109 7.5. Philosophy and the physics of communicational emergence 110 7.6. Emergences and molecular communication in the living 111 7.7. Different considerations about language and the emergence of goal-oriented societies 114 7.7.1. Language, civilizations and human enterprises 115 7.7.2. The myth of Babel, communicating and building 116 7.7.3. Language structures 118 7.7.4. Language levels 120 7.8. Brief notes about the semantic field 121 Chapter 8. The Computer, from Physics to Biology 123 8.1. Computer and information in the 21st Century science 123 8.2. The research by David Deutsch and Seth Lloyd concerning the quantum calculator 125 8.3. Seth Lloyd and quantum order in the universe 128 8.4. Going beyond the theory of information: the resonance coupling principle 131 8.5. From the biological to the physical 132 8.5.1. From biology to informed physics: an original pathway offered by Paul Davies 133 8.5.2. Biology and networks: questioning emergence with information and entropy 134 8.5.3. Information and networks, theoretical limitations and metaphysical options 137 8.6. Kronos, Telos and the evolution of living emergences 138 Chapter 9. Time Philosophies: Kronos, Telos, Kosmos 141 9.1. Time is plural, as it is enigmatic 141 9.2. The “qualities” of time: an excursion through Eastern thought 144 9.3. Aristotle 147 9.4. Leibniz 149 9.5. Being, time, things 152 9.6. Things in modern science 155 9.7. Hegel, Nietzsche, Heidegger: three prophets of time 158 9.7.1. Hegel and the dialectic resolution of Kronos with Telos 159 9.7.2. Nietzsche and Kronos transmuted into Telos 160 9.7.3. Husserl, the world and Kosmos-based objects 161 9.7.4. Heidegger and the quest for Kosmos 162 9.7.5. Emerging Logos and Telos in the end times 164 Chapter 10. The Arrows of Time and Emergence 167 10.1. The three categories of time and contemporary physics 167 10.2. Noise, temperature, entropy, time arrow 170 10.3. The effect of temperature on emerging order 173 10.4. Order and the arrow of time 176 10.4.1. Entropy and disorder 176 10.4.2. Prigogine and irreversibility 178 10.5. From Kronos to Telos, irreversibility and the two arrows of material time 181 10.5.1. The RHS from the Brussels-Austin school 181 10.5.2. The two orientations of time and the metamorphosis of modern physics 184 10.5.3. The arrow of Kosmos; mechanics and thermodynamics 187 10.6. Kosmos, Kronos and Telos 188 10.7. Concluding remark on physics and things 191 10.8. From the history of black holes to the light of time 193 Chapter 11. Mesoscopic and Macroscopic 199 11.1. Between infrascopic and macroscopic quantum, the mesoscopic order 199 11.2. Horizontal and vertical emergences 202 11.3. The signals associated with emergences 204 11.3.1. Infrascopic fundamental matter and quantum interactions 205 11.3.2. Condensed matter and mesophysical emergences 205 11.3.3. Molecular matter 206 11.3.4. Life at the mesoscopic level 206 11.3.5. Macrobiology and macroscopic emergences 208 11.3.6. Human societies and communicating forms 210 11.3.7. Ordering and interpreting systems in human emergences 211 11.4. Biosemiotics, emergences and evolution 212 11.5. Physicalism and mental processes 217 11.6. Some considerations on emergent worlds 219 11.6.1. Gravity, AdS/CFT, megascopic emergence cosmos 219 11.6.2. The emergence of the sacred and Being 221 11.7. The order of time at the four scales of the universe 222 Chapter 12. Epilogue on Forthcoming Science 225 12.1. Modernity is achieved 225 12.2. Unfinished notes on the cosmos, physics and metaphysics 228 12.3. Communicational emergences represented in a figure 230 12.4. The metamorphosis of the subject 231 12.5. From Kosmos to Logos 232 12.6. Epilogue on three ongoing scientific revolutions 233 Conclusion 237 Bibliography 241 Index 245
£125.06
ISTE Ltd and John Wiley & Sons Inc Introduction to Quantum Mechanics 2:
Book SynopsisQuantum mechanics is the foundation of modern technology, due to its innumerable applications in physics, chemistry and even biology. This second volume studies Schrödinger�s equation and its applications in the study of wells, steps and potential barriers. It examines the properties of orthonormal bases in the space of square-summable wave functions and Dirac notations in the space of states. This book has a special focus on the notions of the linear operators, the Hermitian operators, observables, Hermitian conjugation, commutators and the representation of kets, bras and operators in the space of states. The eigenvalue equation, the characteristic equation and the evolution equation of the mean value of an observable are introduced. The book goes on to investigate the study of conservative systems through the time evolution operator and Ehrenfest�s theorem. Finally, this second volume is completed by the introduction of the notions of quantum wire, quantum wells of semiconductor materials and quantum dots in the appendices.Table of Contents1. Schrödinger�s Equation and its Applications. 2. Hermitian Operator, Dirac�s Notations. 3. Eigenvalues and Eigenvectors of an Observable.
£125.06
Springer Nature Switzerland AG Geometric Multiplication of Vectors: An
Book SynopsisThis book enables the reader to discover elementary concepts of geometric algebra and its applications with lucid and direct explanations. Why would one want to explore geometric algebra? What if there existed a universal mathematical language that allowed one: to make rotations in any dimension with simple formulas, to see spinors or the Pauli matrices and their products, to solve problems of the special theory of relativity in three-dimensional Euclidean space, to formulate quantum mechanics without the imaginary unit, to easily solve difficult problems of electromagnetism, to treat the Kepler problem with the formulas for a harmonic oscillator, to eliminate unintuitive matrices and tensors, to unite many branches of mathematical physics? What if it were possible to use that same framework to generalize the complex numbers or fractals to any dimension, to play with geometry on a computer, as well as to make calculations in robotics, ray-tracing and brain science? In addition, what if such a language provided a clear, geometric interpretation of mathematical objects, even for the imaginary unit in quantum mechanics? Such a mathematical language exists and it is called geometric algebra. High school students have the potential to explore it, and undergraduate students can master it. The universality, the clear geometric interpretation, the power of generalizations to any dimension, the new insights into known theories, and the possibility of computer implementations make geometric algebra a thrilling field to unearth.Table of ContentsBasic Concepts.- Euclidean 3D Geometric Algebra.- Applications.- Geometric Algebra and Matrices.- Appendix.- Solutions for Some Problems.- Problems.- Why Geometric Algebra?.- Formulae.- Literature.- References.
£31.49
Springer Nature Switzerland AG Mathematics of Quantum Computing: An Introduction
Book SynopsisThis textbook presents the elementary aspects of quantum computing in a mathematical form. It is intended as core or supplementary reading for physicists, mathematicians, and computer scientists taking a first course on quantum computing. It starts by introducing the basic mathematics required for quantum mechanics, and then goes on to present, in detail, the notions of quantum mechanics, entanglement, quantum gates, and quantum algorithms, of which Shor's factorisation and Grover's search algorithm are discussed extensively. In addition, the algorithms for the Abelian Hidden Subgroup and Discrete Logarithm problems are presented and the latter is used to show how the Bitcoin digital signature may be compromised. It also addresses the problem of error correction as well as giving a detailed exposition of adiabatic quantum computing. The book contains around 140 exercises for the student, covering all of the topics treated, together with an appendix of solutions.Table of ContentsIntroduction.- Basic Notions of Quantum Mechanics.- Tensor Products and Composite Systems.- Entanglement.- Quantum Gates and Circuits for Elementary Calculations.- On the Use of Entanglement.- Error Correction.- Adiabatic Quantum Computing.- Epilogue Appendices: A Elementary Probability Theory.- B Elementary Arithmetic Operations.- C LANDAU Symbols.- D Modular Arithmetic.- E Continued Fractions.- F Some Group Theory.- G Proof of a Quantum Adiabatic Theorem.- Solutions to Exercises.
£85.49
Springer Nature Switzerland AG Solid State Physics
Book SynopsisThe book has been designed as a textbook for graduate and postgraduate students of physics, material science, and engineering. This is the third edition of the textbook, that is updated to reflect recent works in the field. In this edition, some new topics have been introduced while some of the existing topics like phonons, Drude –Lorentz model, Fermi levels, electrons, and holes, etc. are modified. Moreover, the book has complete information on semiconductor devices like tunnel diode, Gunn diode, photodiode, photoconductive diode, varactor diode, solar cell, LED, semiconductor lasers, and semiconductor detectors. All the chapters have been supplemented by solved and unsolved examples. Some of the chapters illustrate areas of current interest in solid-state physics to give the student practical working knowledge of the subject text in a simple and lucid manner. There is a fair amount of detail in the examples and derivations given in the text. Each section of the book has exercises to reinforce the concepts, and problems have been added at the end of each chapter. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in graduate and postgraduate courses of physics, material science, and engineering.Table of ContentsCrystal Structure.- Chemical Bonding in Solids.- Defects in Solids.- Elecments of Quantum Mechanics.- X-Ray Diffraction.- Lattice Vibrations.- Thermal Properties of Solids.- Free Electron Theory of Metals.- Band Theory.- Semiconductors.- Dielectric Properties of Solids.- Magnetic Properties of Matter.- Magnetic Resonance.- Superconductivity.- Nanomaterials.- Optical Properties.- Semiconductor Devices.
£80.99
Springer Nature Switzerland AG Schrödinger Theory of Electrons: Complementary
Book SynopsisThis book presents a complementary perspective to Schrödinger theory of electrons in an electromagnetic field, one that does not appear in any text on quantum mechanics. The perspective, derived from Schrödinger theory, is that of the individual electron in the sea of electrons via its temporal and stationary-state equations of motion – the ‘Quantal Newtonian’ Second and First Laws. The Laws are in terms of ‘classical’ fields experienced by each electron, the sources of the fields being quantum-mechanical expectation values of Hermitian operators taken with respect to the wave function. Each electron experiences the external field, and internal fields representative of properties of the system, and a field descriptive of its response. The energies are obtained in terms of the fields. The ‘Quantal Newtonian’ Laws lead to physical insights, and new properties of the electronic system are revealed. New mathematical understandings of Schrödinger theory emerge which show the equation to be intrinsically self-consistent. Another complimentary perspective to Schrödinger theory is its manifestation as a local effective potential theory described via Quantal Density Functional theory. This description too is in terms of ‘classical’ fields and quantal sources. The theory provides a rigorous physical explanation of the mapping from the interacting system to the local potential theory equivalent. The complementary perspective to stationary ground state Schrödinger theory founded in the theorems of Hohenberg and Kohn, their extension to the presence of a magnetic field and to the temporal domain – Modern Density Functional Theory -- is also described. The new perspectives are elucidated by application to analytically solvable interacting systems. These solutions and other relevant wave function properties are derived.Table of ContentsIntroduction.- Schrödinger Theory of Electrons: A Complementary Perspective.- Generalization of the Schrödinger Theory of Electrons.- Schrödinger-Pauli Theory of Electrons: A Complementary Perspective.
£113.99
Springer International Publishing AG Jost Functions in Quantum Mechanics: A Unified
Book SynopsisBased on Jost function theory this book presents an approach useful for different types of quantum mechanical problems. These include the description of scattering, bound, and resonant states, in a unified way. The reader finds here all that is known about Jost functions as well as what is needed to fill the gap between the pure mathematical theory and numerical calculations. Some of the topics covered are: quantum resonances, Regge poles, multichannel scattering, Coulomb interaction, Riemann surfaces, multichannel analog of the effective range theory, one- and two-dimensional problems, many-body problems within the hyperspherical approach, just to mention few of them. These topics are relevant in the fields of quantum few-body theory, nuclear reactions, atomic collisions, and low-dimensional semiconductor nanostructures. In light of this, the book is meant for students, who study quantum mechanics, scattering theory, or nuclear reactions at the advanced level as well as for post-graduate students and researchers in the fields of nuclear and atomic physics. Many of the arguments that are traditional for textbooks on quantum mechanics and scattering theory, are covered here in a different way, using the Jost functions. This gives the reader a new insight into the subject, revealing new features of various mathematical objects and quantum phenomena.Trade Review“This book has to be recommended to graduate students and to young researchers as well who want to enter the difficult field of modern scattering theory.” (Giorgio Cattapan, Mathematical Reviews, July, 2023)Table of ContentsChapter 1: The Basic Concepts.- Part I: Single-Channel Problems.- Chapter 2: Schr¨Odinger Equation and its Solutions.- Chapter 3: Riemann Surface and the Spectral Points.- Chapter 4: Scattering States and the S-Matrix.- Chapter 5: Complex Angular Momentum.- Chapter 6: Green’s Functions.- Chapter 7: Short-Range Potential Extending to Infinity.- Chapter 8: Single-Channel Potential with Coulombic Tail.- Part II: Multi-Channel Problems.- Chapter 9: Non-Central Potential.- Chapter 10: Systems with Non-Zero Spin.- Chapter 11: Multi-Channel Schr Odinger Equation.- Chapter 12: Multi-Channel Jost Matrix.- Chapter 13: Riemann Surfaces for Multi-Channel Systems.- Chapter 14: Multi-Channel Problems of Charged Particles.- Chapter 15: Effective-Range Expansion and its Generalizations.- Part III: Special Issues.- Chapter 16: Singular and Low-Dimensional Potentials.- Chapter 17: Miscellaneous Extensions of the Jost Function Approach.- Chapter 18: Some Exactly Solvable Potential Models.- Appendices.- References and Index.
£142.49
