Quantum physics Books

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.

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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.

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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

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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

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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

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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.

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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

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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.

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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

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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

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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.

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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.

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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.

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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.

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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.

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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.

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Book SynopsisThis book provides a comprehensive introduction to photoelectron angular distributions and their use in the laboratory to study light-matter interactions. Photoelectron angular distribution measurements are useful because they can shed light on atomic and molecular electronic configurations and system dynamics, as well as provide information about quantum transition amplitudes and relative phases that are not obtainable from other types of measurements. For example, recent measurements of molecular-frame photoelectron angular distributions have been used to extract photoelectron emission delays in the attosecond range which can provide ultra-sensitive maps of molecular potentials. Additionally, photoelectron angular distribution measurements are an essential tool for studying negative ions. Here, the author presents a detailed, yet easily accessible, theoretical background necessary for experimentalists performing photoelectron angular distribution measurements to better understand their results. The various physical influences on photoelectron angular distributions are revealed through analytical models with the use of angular momentum coupling algebra and spherical tensor operators. The classical and quantum treatments of photoelectron angular distributions are covered clearly and systematically, and the book includes, as well, a chapter on relativistic interactions. Furthermore, the primary methods used to measure photoelectron angular distributions in the laboratory, such as photodetachment electron spectroscopy, velocity-map imaging, and cold target recoil ion momentum spectroscopy, are described. This book features introductory material as well as new insights on the topic, such as the use of angular momentum transfer theory to understand the process of photoelectron detachment in atoms and molecules. Including key derivations, worked examples, and additional exercises for readers to try on their own, this book serves as both a critical guide for young researchers entering the field and as a useful reference for experienced practitioners.Table of ContentsChapter 1. Introduction.- Chapter 2. Angular Momentum in Quantum Mechanics.- Chapter 3. Classical Model of Photoelectron Angular Distributions.- Chapter 4. Quantum Treatment of Photoelectron Angular Distributions (Dipole Approximation).- Chapter 5. Higher-order Multipole Terms in Photoelectron Angular Distributions.- Chapter 6. Relativistic Theory of Photoelectron Angular Distributions.- Chapter 7. Angular Momentum Transfer Theory.- Chapter 8. Molecular Photoelectron Angular Distributions.- Chapter 9. Measuring Photoelectron Angular Distributions in the Laboratory.- Chapter 10. Applications of Photoelectron Angular Distribution Measurements.

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Book SynopsisThis book presents the most common types of instabilities arising in classical field theories, namely tachyonic, Laplacian, ghost-like or strong coupling instabilities, also commenting on their quantum implications. The authors provide a detailed account on the Ostrogradski theorem and its implications for higher-order time-derivative field theories. After presenting the general concepts and formalism, they dive into its applications to particular field theories, using mainly modified gravity theories as examples. The book is intended for advanced undergraduate/graduate students, but can also be useful for researchers, for having a unified exposition of general results on instabilities in field theory and examples of their applications.Table of ContentsIntroduction to instabilities and some relevant examples.- Ostrogradski theorem and ghosts.- Examples of instabilities in gravity theories.- References.- Solutions.

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Book SynopsisChapter 1. Quantum Degenerate Gases.-Chapter 2. Trapping and Cooling of Atoms.- Chapter 3. Ultracold Atoms as Weakly-Correlated Systems.- Chapter 4. Ultracold Atoms as Strongly-Correlated Systems.- Chapter 5. Quantum Coherence with Ultracold Atoms.

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Book SynopsisIntroduction.- Classical and Modern Cryptography.- Quantum Algorithms.- Quantum Cryptography.- Quantum Computing Applications.- Future Directions and Open Challenges.-  Conclusion.

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Book Synopsis

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Book SynopsisThis text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.Trade Review“The book presents a large variety of important subjects, including the basic principles of quantum mechanics … . This good book is recommended for mathematicians, physicists, philosophers of physics, researchers, and advanced students in mathematics and physics, as well as for readers with some elementary physics, multivariate calculus and linear algebra courses.” (Michael M. Dediu, Mathematical Reviews, June, 2018)Table of ContentsPreface.- 1 Introduction and Overview.- 2 The Group U(1) and its Representations.- 3 Two-state Systems and SU(2).- 4 Linear Algebra Review, Unitary and Orthogonal Groups.- 5 Lie Algebras and Lie Algebra Representations.- 6 The Rotation and Spin Groups in 3 and 4 Dimensions.- 7 Rotations and the Spin 1/2 Particle in a Magnetic Field.- 8 Representations of SU(2) and SO(3).- 9 Tensor Products, Entanglement, and Addition of Spin.- 10 Momentum and the Free Particle.- 11 Fourier Analysis and the Free Particle.- 12 Position and the Free Particle.- 13 The Heisenberg group and the Schrödinger Representation.- 14 The Poisson Bracket and Symplectic Geometry.- 15 Hamiltonian Vector Fields and the Moment Map.- 16 Quadratic Polynomials and the Symplectic Group.- 17 Quantization.- 18 Semi-direct Products.- 19 The Quantum Free Particle as a Representation of the Euclidean Group.- 20 Representations of Semi-direct Products.- 21 Central Potentials and the Hydrogen Atom.- 22 The Harmonic Oscillator.- 23 Coherent States and the Propagator for the Harmonic Oscillator.- 24 The Metaplectic Representation and Annihilation and Creation Operators, d = 1.- 25 The Metaplectic Representation and Annihilation and Creation Operators, arbitrary d.- 26 Complex Structures and Quantization.- 27 The Fermionic Oscillator.- 28 Weyl and Clifford Algebras.- 29 Clifford Algebras and Geometry.- 30 Anticommuting Variables and Pseudo-classical Mechanics.- 31 Fermionic Quantization and Spinors.- 32 A Summary: Parallels Between Bosonic and Fermionic Quantization.- 33 Supersymmetry, Some Simple Examples.- 34 The Pauli Equation and the Dirac Operator.- 35 Lagrangian Methods and the Path Integral.- 36 Multi-particle Systems: Momentum Space Description.- 37 Multi-particle Systems and Field Quantization.- 38 Symmetries and Non-relativistic Quantum Fields.- 39 Quantization of Infinite dimensional Phase Spaces.- 40 Minkowski Space and the Lorentz Group.- 41 Representations of the Lorentz Group.- 42 The Poincaré Group and its Representations.- 43 The Klein-Gordon Equation and Scalar Quantum Fields.- 44 Symmetries and Relativistic Scalar Quantum Fields.- 45 U(1) Gauge Symmetry and Electromagnetic Field.- 46 Quantization of the Electromagnetic Field: the Photon.- 47 The Dirac Equation and Spin-1/2 Fields.- 48 An Introduction to the Standard Model.- 49 Further Topics.- A Conventions.- B Exercises.- Index.

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Book SynopsisThis book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.This book is Open Access under a CC BY licence. Trade Review“Quantum theory has frequent applications in the subjects of quantum information theory and quantum optics. The purpose of this book is to present the foundations of quantum theory in connection with classical physics, from the point of view of classical-quantum duality. … This good book is recommended for mathematicians, physicists, philosophers of physics, researchers and advanced students in this field.” (Michael M. Dediu, Mathematical Reviews, Decemeber, 2017)Table of ContentsIntroduction.- Part I Co(X) and B(H): Classical physics on a finite phase space.- Quantum mechanics on a finite-dimensional Hilbert space.- Classical physics on a general phase space.- Quantum physics on a general Hilbert space.- Symmetry in quantum mechanics.- Part II Between Co(X) and B(H): Classical models of quantum mechanics.- Limits: Small hbar.- Limits: large N.- Symmetry in algebraic quantum theory.- Spontaneous Symmetry Breaking.- The Measurement Problem.- Topos theory and quantum logic.- Appendix A: Finite-dimensional Hilbert spaces.- Appendix B: Basic functional analysis.- Appendix C: Operator algebras.- Appendix D: Lattices and logic.- Appendix E: Category theory and topos theory.- References.

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Book SynopsisThis book tells the story of the second quantum revolution which will shape the 21st century as much as the first quantum revolution shaped the 20th century. It provides unique orientation in today's discussion and the latest progress on the interpretation of quantum physics and its further technological potential. As you read this book the first prototypes of this revolution are being built in laboratories worldwide. Super-technologies such as nanotechnology, quantum computers, quantum information processing, and others will soon shape our daily lives, even if physicists themselves continue to disagree on how to interpret the central theory of modern physics. The book will thus also touch on the profound philosophical questions at the heart of quantum mechanics.Table of ContentsPrologue: The white rabbit.- Part 1: Quantum 2.0 – The second technological revolution arising from the quantum world: Mighty power – How a theory of the microcosm changed our world.-There‘s plenty of room at the bottom – A new generation of quantum technologies.- Technology on the smallest scales – The possibilities of nanotechnology.- Incredibly fast – From digital to the quantum computer.- Part 2: Quantum Worlds – The bizarre in the very small: Contradictory atoms – Philosophical problems with the smallest building blocks of nature.- Natura facit saltus – On quantum jumps and particles being made out of nothing.- Tertium datur – Wave and particles at the same time.- As well as neither/-nor – Superposition: how things can be here and there at the same time.- Loss of identity – The New Reality Concept of Quantum Physics and its Consequences.- Part 3: From Quantum Field Theories to a "Theory of Everything" – All matter dissolves: Negative energies and the electron spin – Combining the theory of relativity to produce a new quantum theory.- Quantum field theories – All matter dissolves.- Infinity minus infinity gives something finite – How physicists learnt to deal with infinitely large values in the infinitely small.- More and more particles – From the particle zoo to the standard model of elementary particle physics.- Einstein does not fit – The fundamental problem in physics today.- Part 4: Cutting across philosophical, aesthetic, and spiritual, frames of thought: The Path towards Substancelessness – Breaking with 2,600 years of philosophical thought.- A New Understanding of Truth – How quantum physics made absolute reality disappear, and with it absolute truth.- The eternal interplay – Surprising overlaps between quantum physics and Buddhism.- Symmetries – Beauty in the House of Physics.- Quantum Consciousness and the Tao of Physics - On quantum holism, quantum healing, and other quantum nonsense.- Quantum physics and faith– Explaining the inexplicable.- Part 5: Entanglement – getting to the crux of the matter: The destinies of cats – The quantum physical measurement problem.- Wigner´s Friend – Quantum physics and consciousness.- EPR and Hidden Variables – The debate about spooky action at a distance.- The experimental resolution of the Bohr- Einstein debate – How entangled particles made their way from theory into practice.- The Age of Entanglement – From spooks to a new quantum revolution.- Schrödinger‘s cat is alive – The path back to classical physics.- Part 6: The future – Where are we going?: Quantum Revolution 2.0 – When nanobots and quantum computers become part of our everyday lives.

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Book SynopsisDie Festkörperphysik ist eines der großen Hauptgebiete der heutigen Physik. Der Festkörper stellt mit seinen verwickelten elektrischen, optischen, thermischen und magnetischen Eigenschaften ein äußerst reizvolles Objekt moderner Grundlagen­ forschung dar. In der Tat gelingt es hier, die oft sehr komplizierten Erscheinungen aufzuklären und bis in die Details hinein zu verfolgen. Das damit verbundene tief­ greifende Verständnis der physikalischen Vorgänge im Festkörper führt darüber­ hinaus zu äußerst wichtigen Anwendungen, z. B. in der Nachrichten-und Computer­ technik. Der Studierende, der sich in dieses Gebiet einarbeiten will, stellt allerdings sehr rasch fest, daß hier in großem Umfang Begriffsbildungen und Methoden der Quantenfeld­ theorie verwendet werden. Diese Methoden gestatten es nicht nur, die physikalischen Vorgänge im Festkörper in eleganter Weise zu beschreiben, sondern sie haben auch zu grundsätzlich neuen Erkenntnissen geführt. Als hervorragendes Beispiel sei hier nur die Erklärung der Supraleitung erwähnt. Andererseits wird dem Studierenden in einer Kursvorlesung, etwa der Quanten­ mechanik, kaum die Möglichkeit geboten, dieses wichtige Gebiet kennenzulernen. Aufgabe dieses Buches soll es sein, diese Lücke zu schließen, indem es den Leser in einfacher Weise an die Begriffsbildungen und Methoden der Quantenfeldtheorie her­ anführt. So sollte ein Leser, der mit den mathematischen Kenntnissen der ersten drei Semes·ter und den Grundbegriffen der Quantenmechanik vertraut ist, ohne weiteres in der Lage sein, sich mit Hilfe dieses Buches in die Quantenfeldtheorie des Fest­ körpers einzuarbeiten.Table of ContentsI. Einleitung.- § 1 Einführung und Übersicht.- § 2 Einige Grundbegriffe der klassischen Mechanik.- II. Harmonische Oszillatoren.- § 3 Der quantenmechanische Oszillator: Erzeugungs- und Vernichtungsoperatoren.- § 4 Die Berechnung von Erwartungswerten.- § 5 Vom Umgang mit Bose-Operatoren: Wir lernen einige Tricks.- § 6 Der verschobene harmonische Oszillator: Vorbild für elementare Anregungen im Festkörper.- III. Feldquantisierung.- § 7 Die lineare Atomkette: klassische Behandlung.- § 8 Die lineare Atomkette: quantentheoretische Behandlung. Phononen.- § 9 Übergang zum Kontinuum: klassisch.- § 10 Übergang zum Kontinuum: quantentheoretisch. Phononen.- § 11 Dreidimensionale Probleme: Quantisierung der skalaren Wellengleichung und des elektromagnetischen Feldes. Photonen.- § 12 Quantisierung des Schrödingerschen Wellenfeldes der Bose-Statistik (2. Quantelung). Bosonen.- § 13 Quantisierung des Schrödingerschen Wellenfeldes der Fermi-Dirac-Statistik. Fermionen.- § 14 Vom Umgang mit Fermi-Operatoren.- § 15 Die Wechselwirkung zwischen Feldern: seiltanzende Elektronen.- § 16 Methodische Kunstbegriffe: das Wechselwirkungsbild und das Heisenbergbild.- IV. Elektronen im starren Gitter.- § 17 Elektronen im Kristallgitter: ein kurzer Abriß der Blochschen Theorie.- § 18 Die Methode der scheinbaren Masse.- § 19 Wannierfunktionen: Wellenpakete aus Blochfunktionen.- § 20 Elektronen im Kristallgitter: Formulierung des Mehrkörperproblems. Der Hartree-Fock-Ansatz.- § 21 Defektelektronen.- § 22 Die Wechselwirkung zwischen Elektronen und Defektelektronen.- § 23 Exzitonen mit großem Bahnradius (Wannier-Exzitonen).- § 24 Frenkel-Exzitonen.- § 25 Elektronische Polarisationswellen.- § 26 Exzitonenmaterie.- § 27 Plasmonen.- § 28 Spinwellen: Magnonen.- V. Elektronen in Wechselwirkung mit Gitterschwingungen.- § 29 Fröhlichs Hamiltonoperator für die Wechselwirkung zwischen Elektronen und Phononen.- § 30 Zeitabhängige Störungstheorie 1. Ordnung. Spontane und induzierte Emission sowie Absorption von Phononen. Darstellung durch Feynman-Graphen..’.- § 31 Der Elektrische Widerstand.- § 32 Zeitabhängige Störungstheorie 2.Ordnung: Selbstenergie, Massenrenomierung.- § 33 Störungstheorie höherer Ordnung.- § 34 Theorem über die exakte Form der Lösung.- § 35 Das Fröhlich-Polaron. Selbstenergie und renormierte Masse.- § 36 Die effektive Wechselwirkung zwischen Polaronen.- VI. Greensche Funktionen.- § 37 Störungstheorie im Ortsraum. Beispiel für das Auftreten Greenscher Funktionen.- § 38 Ausbreitungsfunktion, Propagator, Greensche Funktion: immer das Gleiche.- § 39 Beispiele von Gleichungen für Greensche Funktionen und deren Lösung.- VII. Supraleitung.- § 40 Einige grundlegende experimentelle Tatsachen der Supraleitung.- § 41 Theorie der Supraleitung: Herleitung der Fröhlich-Wechselwirkung zwischen den Elektronen.- § 42 Der Grundzustand des Supraleiters nach der Bardeen-Cooper-Schrieffer-Theorie.- § 43 Angeregte Zustände des Supraleiters.- VIII. Elektronen in Wechselwirkung mit dem quantisierten Lichtfeld.- § 44 Die Wechselwirkung zwischen Licht und Materie: Der Hamiltonoperator 293.- § 45 Polaritonen.- Weiterführende Literatur.

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Book Synopsis

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Book SynopsisIt is unanimously accepted that the quantum and the classical descriptions of the physical reality are very different, although any quantum process is "mysteriously" transformed through measurement into an observable classical event. Beyond the conceptual differences, quantum and classical physics have a lot in common. And, more important, there are classical and quantum phenomena that are similar although they occur in completely different contexts. For example, the Schrödinger equation has the same mathematical form as the Helmholtz equation, there is an uncertainty relation in optics very similar to that in quantum mechanics, and so on; the list of examples is very long. Quantum-classical analogies have been used in recent years to study many quantum laws or phenomena at the macroscopic scale, to design and simulate mesoscopic devices at the macroscopic scale, to implement quantum computer algorithms with classical means, etc. On the other hand, the new forms of light – localized light, frozen light – seem to have more in common with solid state physics than with classical optics. So these analogies are a valuable tool in the quest to understand quantum phenomena and in the search for new (quantum or classical) applications, especially in the area of quantum devices and computing.Trade ReviewFrom the reviews: "The main role of quantum classical analogies presented in ten distinct chapters is to shed some light on the genuine significance of the quantum and classical worlds. … The book addresses a large category of readers, especially graduates and PhD students … . The book is also useful for researchers working in advanced topics … . It can be used as an additional source for a course on quantum mechanics … . The hard cover book is nicely edited … ." (Roland Carchon, Physicalia, Vol. 57 (3), 2005) "The authors … devote their new book to the striking analogies between classical and quantum physics. … the authors wish to show that the classical and quantum worlds share many common concepts despite striking differences. … The wealth of analogies … discovered and presented in ten distinct chapters sheds some light on the genuine significance of both the quantum world and its classical counterpart. The book addresses students and researchers alike specialising in the study of quantum devices, atom optics or quantum optics." (Gert Roepstorff, Zentralblatt MATH, Vol. 1093 (19), 2006) "Analogies are a powerful cognitive tool that allow us to make inferences and learn new aspects from the comparison of two things by highlighting their similarities. … It is important to mention that the book is intended to be a catalogue of phenomena shared between classical and quantum physics … . the references given are an invaluable asset. … This book is therefore a very good choice for those interested in bridging ideas from classical physics into the quantum world or vice versa." (Dr. J. Rogel-Salazar, Contemporary Physics, Vol. 46 (6), 2005) "This book develops and explores in a systematic manner a large number of analogs between quantum and classical theories. … It follows closely the recent experimental developments, and for each chapter there is a large number of current references. … It will be very valuable for a large category of readers ranging from graduate and Ph. D. students to researchers working in these areas, and on to teachers looking for nontrivial modern applications and developments in both quantum and classical physics." (Vitor R. Vieira, Mathematical Reviews, Issue 2007 c)Table of Contents1 Introduction.- 2 Analogies Between Ballistic Electrons and Electromagnetic Waves.- 3 Electron/Electromagnetic Multiple Scattering and Localization.- 4 Acoustic Analogies for Quantum Mechanics.- 5 Optical Analogs for Multilevel Quantum Systems.- 6 Particle Optics.- 7 Quantum/Classical Nonlinear Phenomena.- 8 Quantum/Classical Phase Space Analogies.- 9 Analogies Between Quantum and Classical Computing.- 10 Other Quantum/Classical Analogies.- References.

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Book Synopsis"This book gives a solid understanding of the basic concepts and results of quantum mechanics including the historical background and philosophical questions...Many worked examples serve to illustrate the material while biographical and historical footnotes round off the content." Zentralblatt MATHTable of Contents1 The Quantization of Physical Quantities.- 1.1 Light Quanta.- 1.2 The Photoelectric Effect.- 1.3 The Compton Effect.- 1.4 The Ritz Combination Principle.- 1.5 The Franck-Hertz Experiment.- 1.6 The Stern-Gerlach Experiment.- 1.7 Biographical Notes.- 2 The Radiation Laws.- 2.1 A Preview of the Radiation of Bodies.- 2.2 What is Cavity Radiation?.- 2.3 The Rayleigh-Jeans Radiation Law: The Electromagnetic Eigenmodes of a Cavity.- 2.4 Planck’s Radiation Law.- 2.5 Biographical Notes.- 3 Wave Aspects of Matter.- 3.1 De Broglie Waves.- 3.2 The Diffraction of Matter Waves.- 3.3 The Statistical Interpretation of Matter Waves.- 3.4 Mean (Expectation) Values in Quantum Mechanics.- 3.5 Three Quantum Mechanical Operators.- 3.6 The Superposition Principle in Quantum Mechanics.- 3.7 The Heisenberg Uncertainty Principle.- 3.8 Biographical Notes.- 4 Mathematical Foundations of Quantum Mechanics I.- 4.1 Properties of Operators.- 4.2 Combining Two Operators.- 4.3 Bra and Ket Notation.- 4.4 Eigenvalues and Eigenfunctions.- 4.5 Measurability of Different Observables at Equal Times.- 4.6 Position and Momentum Operators.- 4.7 Heisenberg’s Uncertainty Relations for Arbitrary Observables.- 4.8 Angular-Momentum Operators.- 4.9 Kinetic Energy.- 4.10 Total Energy.- 4.11 Biographical Notes.- 5 Mathematical Supplement.- 5.1 Eigendifferentials and the Normalization of Eigenfunctions for Continuous Spectra.- 5.2 Expansion into Eigenfunctions.- 6 The Schrödinger Equation.- 6.1 The Conservation of Particle Number in Quantum Mechanics.- 6.2 Stationary States.- 6.3 Properties of Stationary States.- 6.4 Biographical Notes.- 7 The Harmonic Oscillator.- 7.1 The Solution of the Oscillator Equation.- 7.2 The Description of the Harmonic Oscillator by Creation and Annihilation Operators.- 7.3 Properties of the Operators â and â+.- 7.4 Representation of the Oscillator Hamiltonian in Terms of â and â+.- 7.5 Interpretation of â and â+.- 7.6 Biographical Notes.- 8 The Transition from Classical to Quantum Mechanics.- 8.1 Motion of the Mean Values.- 8.2 Ehrenfest’s Theorem.- 8.3 Constants of Motion, Laws of Conservation.- 8.4 Quantization in Curvilinear Coordinates.- 8.5 Biographical Notes.- 9 Charged Particles in Magnetic Fields.- Coupling to the Electromagnetic Field.- 9.1 The Hydrogen Atom.- 9.2 Three-Dimensional Electron Densities.- 9.3 The Spectrum of Hydrogen Atoms.- 9.4 Currents in the Hydrogen Atom.- 9.5 The Magnetic Moment.- 9.6 Hydrogen-like Atoms.- 9.7 Biographical Notes.- 10 The Mathematical Foundations of Quantum Mechanics II.- 10.1 Representation Theory.- 10.2 Representation of Operators.- 10.3 The Eigenvalue Problem.- 10.4 Unitary Transformations.- 10.5 The S Matrix.- 10.6 The Schrödinger Equation in Matrix Form.- 10.7 The Schrödinger Representation.- 10.8 The Heisenberg Representation.- 10.9 The Interaction Representation.- 10.10 Biographical Notes.- 11 Perturbation Theory.- 11.1 Stationary Perturbation Theory.- 11.2 Degeneracy.- 11.3 The Ritz Variational Method.- 11.4 Time-Dependent Perturbation Theory.- 11.5 Time-Independent Perturbation.- 11.6 Transitions Between Continuum States.- 11.7 Biographical Notes.- 12 Spin.- 12.1 Doublet Splitting.- 12.2 The Einstein-de Haas Experiment.- 12.3 The Mathematical Description of Spin.- 12.4 Wave Functions with Spin.- 12.5 The Pauli Equation.- 12.6 Biographical Notes.- 13 A Nonrelativistic Wave Equation with Spin.- 13.1 The Linearization of the Schrödinger Equation.- 13.2 Particles in an External Field and the Magnetic Moment.- 14 Elementary Aspects of the Quantum-Mechanical Many-Body Problem.- 14.1 The Conservation of the Total Momentum of a Particle System.- 14.2 Centre-of-Mass Motion of a System of Particles in Quantum Mechanics.- 14.3 Conservation of Total Angular Momentum in a Quantum-Mechanical Many-Particle System.- 14.4 Small Oscillations in a Many-Particle System.- 14.5 Biographical Notes.- 15 Identical Particles.- 15.1 The Pauli Principle.- 15.2 Exchange Degeneracy.- 15.3 The Slater Determinant.- 15.4 Biographical Notes.- 16 The Formal Framework of Quantum Mechanics.- 16.1 The Mathematical Foundation of Quantum Mechanics: Hilbert Space.- 16.2 Operators in Hilbert Space.- 16.3 Eigenvalues and Eigenvectors.- 16.4 Operators with Continuous or Discrete-Continuous (Mixed) Spectra.- 16.5 Operator Functions.- 16.6 Unitary Transformations.- 16.7 The Direct-Product Space.- 16.8 The Axioms of Quantum Mechanics.- 16.9 Free Particles.- 16.10 A Summary of Perturbation Theory.- 17 Conceptual and Philosophical Problems of Quantum Mechanics..- 17.1 Determinism.- 17.2 Locality.- 17.3 Hidden-Variable Theories.- 17.4 Bell’s Theorem.- 17.5 Measurement Theory.- 17.6 Schrödinger’s Cat.- 17.7 Subjective Theories.- 17.8 Classical Measurements.- 17.9 The Copenhagen Interpretation.- 17.10 Indelible Recording.- 17.11 The Splitting Universe.- 17.12 The Problem of Reality.

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Book SynopsisWe are pleased by the positive resonance of our book which now necessitates a fourth edition. We have used this opportunity to implement corrections of misprints and amendments at several places, and to extend and improve the discussion of many of the exercises and examples. We hope that our presentation of the method of equivalent photons (Example 3. 17), the form factor of the electron (Example 5. 7), the infrared catastrophe (Example 5. 8) and the energy shift of atomic levels (Example 5. 9)arenow even better to understand. The new Exercise 5. 10 shows in detail how to arrive at the non-relativistic limit for the calculation of form factors. Moreover, we have brought up-to-date the Biographical Notes about physicists who have contributed to the dev- opment of quantum electrodynamics, and references to experimental tests of the t- ory. For example, there has been recent progress in the determination of the electric and magnetic form factors of the proton (discussed in Exercise 3. 5 on the Rosenbluth formula) and the Lamb shift of high-Z atoms (discussed in Example 5. 9 on the energy shift of atomic levels), while the experimental veri cation of the birefringence of the QED vacuum in a strong magnetic eld (Example 7. 8) remains unsettled and is a topic of active ongoing research.Trade ReviewFrom the reviews of the third edition: "Quantum electrodynamics (QED) nowadays is considered to be physics’ most precise theory beneath the theory of general relativity. … Greiner’s and Reinhardt’s book provides both teachers and students with all that is necessary to understand QED from its origin. And to the best of my knowledge, it is one of the few books that really do so. … as a reference book, it forms a good companion to any other book on the shelf to show exactly how things are done." (T. Beier, Contemporary Physics, Vol. 45 (3), 2004) "This completely revised and corrected new edition provides several new examples and exercises to enable deeper insight to formalism and application of Quantum electrodynamics. It is a thorough introductory text providing all necessary mathematical tools together with many examples and worked problems." (Revista Espanola de Fisica, Vol. 17 (6), 2003) "The particular volume on quantum electrodynamics was first published in 1992, with a second edition in 1994 and now a third one at the end of 2002. … I have used the former edition(s) of this particular volume in a course on QED and it is a very good source to find all the details. … The books of Greiner … have owned their specific place in the literature on theoretical physics and this volume fits fully in that scheme." (Kris Heyde, Physicalia, Vol. 25 (4), 2003)Table of ContentsPropagators and Scattering Theory.- The Propagators for Electrons and Positrons.- Quantum-Electrodynamical Processes.- Summary: The Feynman Rules of QED.- The Scattering Matrix in Higher Orders.- Two-Particle Systems.- Quantum Electrodynamics of Strong Fields.- Quantum Electrodynamics of Spinless Bosons.

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Book SynopsisDer Grundkurs Theoretische Physik deckt in 7 Bänden die im Diplom- und Bachelor/Master-Studium maßgeblichen Gebiete ab und vermittelt das im jeweiligen Semester benötigte theoretisch-physikalische Rüstzeug. Der erste Teil von Band 5 beginnt mit einer Begründung der Quantenmechanik und der Zusammenstellung ihrer formalen Grundlagen, um dann Konzepte und Begriffsbildungen an Modellsystemen zu illustrieren. Der Band enthält Übungsaufgaben und Kontrollfragen zur Vertiefung des Stoffs. Die überarbeitete und ergänzte Neuauflage ist zweifarbig gestaltet.Table of ContentsInduktive Begründung der Wellenmechanik.- Schrödinger-Gleichung.- Grundlagen der Quantenmechanik (Dirac-Formalismus).- Einfache Modellsysteme.- Lösungen der Übungsaufgaben.

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Book SynopsisDie berühmte Vorlesung von Freeman Dyson - nun erstmals auf Deutsch. In den 1940er Jahren zeigte Freeman Dyson die Äquivalenz zwischen den beiden Formulierungen der QED - des Pfadintegralansatzes von Richard Feynman und der Variationsmethoden von Julian Schwinger - und bewies somit die Konsistenz der QED. Dieses Buch beinhaltet die wertvollen - nie zuvor auf Deutsch publizierten - Vorlesungen über Quantenfeldtheorie, die Dyson an der Cornell Universität 1951 gehalten hat. Der Theoretiker Edwin Thompson Jaynes bemerkte dazu: "Für eine Generation von Physikern waren diese Vorlesungen ein Gewinn: klarer und besser motiviert als Feynmans Vorlesungen, und schneller und kompakter als Schwingers." Zukünftige Leser werden diese Vorlesungen ebenfalls mit großem Genuss lesen und von dem klaren Stil profitieren, der für Dyson stets so charakteristisch gewesen ist.Aus dem Inhaltsverzeichnis: 1 - Die Diracgleichung, 2 - Streuprobleme und die Born-Approximation, 3 - Die klassische und quantenmechanische Feldtheorie, 4 - Beispiele quantisierter Feldtheorien (Maxwellfeld, Diracelektronen), 5 - Streuprobleme freier Teilchen (Paar Annihilation, Möller-Streuung, Klein-Nishina-Formel), 6 - Allgemeine Theorie der Streuung (Feynman-Graphen, Infrarotkatastrophe), 7 - Streuung an einem statischen Potenzial und experimentelle Ergebnisse.Table of ContentsEinleitung.- Diracs Theorie.- Streuprobleme und Bornsche Näherung.- Feldtheorie.- Quantisierte Feldtheorien.- Freie Teilchen und Streuung.- Allgemeine Streutheorie.- Streuung am statischen Potenzial. ​

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Book SynopsisIn dem vorliegenden Buch werden die Grundlagen der nichtrelativistischen Quantenmechanik ausgehend von einer Diskussion der klassischen Experimente dargestellt und in Bezug zu aktuellen Untersuchungsmethoden gesetzt. Zur Illustration werden Abbildungen aus den Originalarbeiten herangezogen. Das grundlegende mathematische Rüstzeug zur Diskussion quantenmechanischer Fragestellungen wird entwickelt. Alle Gedankengänge und insbesondere die Rechnungen werden ausführlich dargestellt. Die Darstellung im Buch wird durch Aufgaben zu jedem Kapitel und Mathematica-Notebooks ergänzt.Die Mathematica-Notebooks und die Lösungen zu den Aufgaben werden als ergänzendes online-Material bereitgestellt. Table of ContentsTeilchenbild.- Wellenbild.- Elektronenbeugung.- Hohlraumstrahlung und Gitterschwingungen.- Atomspektren.- Teilchen-Wellen-Dualismus.- Zeitunabhängige Schrödingergleichung.- Gebundene Zustände.- Streuzustände.- Näherungsverfahren.- Darstellung und Zeitablauf physikalischer Größen.- Quasistationäre Zustände.- Wasserstoffspektrum.- Der Bahndrehimpuls.- Die radiale Bewegung.- Der Elektronenspin.- Drehimpulsoperatoren.

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Book SynopsisCarsten Kleppel liefert eine verständliche Motivation und Diskussion der Dirac-Gleichung, von der aus mit Hilfe der Feldquantisierung und Störungstheorie die Grundzüge der Quantenelektrodynamik erschlossen werden. Die nach P. A. M. Dirac benannte Gleichung ist eine der größten Errungenschaften der theoretischen Physik des 20. Jahrhunderts und bildete eine wichtige Grundlage der Entwicklung der Quantenelektrodynamik.Table of Contents​Einleitung.- Die Dirac-Gleichung.- Eine Quantentheorie des Lichts.- Feldquantisierung des Dirac-Feldes.- Quantenelektrodynamik.- Zusammenfassung und Ausblick.- Anhang: Längere Rechnungen und Beweise.

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Book Synopsis​Die Quantenmechanik ist eine physikalische Theorie für Objekte des Mikrokosmos, also z.B. für Atome oder Elektronen. Sie hat sich bisher bestens bewährt, führt aber dazu, dass wir diesen Objekten Eigenschaften und Relationen zubilligen müssen, die weder mit unserem gesunden Menschenverstand noch mit den Begriffen der klassischen Physik vereinbar sind. Diese Merkwürdigkeiten werden vorgestellt und ihre Bedeutung für unser Erkenntnisvermögen und für ein Weltbild wird diskutiert.Table of Contents Einleitung.- Emergenz bzw. Supervenienz.- Objekte, Merkmale, Relationen.- Begriffe in der klassischen Physik.- Die Merkwürdigkeiten in der Quantenmechanik.- Resumé.

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Book SynopsisSchon früh im Physikstudium und auch bereits in der Schule machen wir Bekanntschaft mit der klassischen Elektrostatik, Magnetostatik, aber auch der Elektrodynamik. Dabei sind die Maxwell-Gleichungen ein nicht mehr wegzudenkender, wichtiger Teil zur Beschreibung des Zusammenhangs zwischen elektrischen und magnetischen Feldern. Doch was ist, wenn wir weiter gehen, wenn wir den klassischen Pfad verlassen und uns der quantenmechanischen Theorie zuwenden? Finden wir dort unsere Wechselwirkung zwischen Licht und Materie wieder? Gibt es, ähnlich wie die Maxwell-Gleichungen, auch solch prägende Gleichungen?Diese Fragen beschäftigen uns in der vorliegenden Arbeit, wobei dazu zunächst die Korrespondenz der relativistischen Mechanik und relativistischen Quantenmechanik untersucht wird. Weiterführend folgt die Quantisierung von Feldern und diese geht in die Quantenelektrodynamik über. Hier werden, aufgrund des einführenden Charakters, nur Prozesse niedrigster Ordnung betrachtet und ein besonderes Augenmerk liegt auf der Compton-Streuung.Table of ContentsEinleitung.- Von der Klein-Gordon-Gleichung zur Dirac-Gleichung.- Feldquantisierung.- Quantenelektrodynamik.- Fazit und Ausblick.- Literaturverzeichnis.

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Book SynopsisCharacterizing entanglement is an important issue in quantum information, as it is considered to be a resource for many applications such as quantum key distribution or quantum metrology. One useful tool to detect and quantify entanglement are witness operators. A standard way to construct them is based on the fidelity of pure states and mathematically relies on the Schmidt decomposition of vectors. In this book a method to build entanglement witnesses using the Schmidt decomposition of operators is presented. One can show that these are strictly stronger than the fidelity witnesses. Moreover, the concept can be generalized easily to the multipartite case, and one may use it to quantify the dimensionality of entanglement. Finally, this scheme will be used to provide two algorithms that can be combined to improve given witnesses for multiparticle entanglement.Table of ContentsIntroduction.- Physical and mathematical background.- OSD witnesses for bipartite states.- The OSD witness for the multipartite case.- Schmidt number witnesses.- Conclusion and outlook.

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Book SynopsisDer beliebte Grundkurs Theoretische Physik deckt in sieben Bänden alle für das Bachelor-/Master- oder Diplomstudium maßgeblichen Gebiete ab. Jeder Band vermittelt gut durchdacht das im jeweiligen Semester nötige theoretisch-physikalische Rüstzeug. Zahlreiche Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffes. Der zweite Teil des fünften Bandes befasst sich mit Anwendungen und mit dem Ausbau der im ersten Teil entwickelten Konzepte der Quantenmechanik.Die vorliegende neue Auflage enthält einige neue Aufgaben, wurde grundlegend überarbeitet und durch einige Zusatzkapitel zur Streutheorie ergänzt. Sie ermöglicht durch die zweifarbige Darstellung einen sehr übersichtlichen und schnellen Zugriff auf den Lehrstoff.Table of ContentsQuantentheorie des Drehimpulses.- Zentralpotential.- Näherungsmethoden.- Mehr-Teilchen-Systeme.- Streutheorie.- Lösungen der Übungsaufgaben.

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Book SynopsisDas vorliegende Tutorium richtet sich an alle, die endlich einmal von der Pike auf die Physik und Mathematik der Quantenmechanik verstehen wollen: Was genau ist eigentlich ein Hilbert-Raum? Was ist ein hermitescher Operator? Ein Tensorprodukt? Ein verschränkter Zustand? Inwiefern sind Wellenfunktionen Vektoren? Das Buch behandelt den Stoff der entsprechenden Kursvorlesung im Rahmen der theoretischen Physik einprägsam und auf eine gut verständliche Weise. Es konzentriert sich dabei auf die allgemeinen Postulate der Quantenmechanik und geht auch auf die Fragestellung hinsichtlich der Interpretation der Quantenmechanik ein.Jeder Schritt und jeder neue Begriff wird anhand von einfachen Beispielen erläutert. Der Autor legt dabei großen Wert auf die Klarheit der verwendeten Mathematik - etwas, das er und viele Studenten in anderen Lehrbüchern bislang oft vermissen mussten. Durch diesen Schwerpunkt ist das Buch auch sehr gut für Mathematiker geeignet, die sich mit dem Thema auseinandersetzen wollen.In der Prüfungsvorbereitung eignet sich das Buch besonders gut zur Klärung von Begriffen und Verständnisfragen. Die im Text eingestreuten „Fragen zum Selbstcheck“ und Übungsaufgaben mit Lösungen unterstützen das Lernen zusätzlich.In der zweiten, überarbeiteten Auflage wurde u.a. das Kapitel „Quantenpandämonium“ ergänzt. Hier werden verschiedene erstaunliche Quantenphänomene (beispielsweise Delayed-Choice Experiment, Wechselwirkungsfreie Messung, Quantenradierer) und das Kochen-Specker Theorem diskutiert.Trade ReviewFrom the book reviews:“It is a publication of a great methodological work made by an experienced tutor. … The book is addressed to students studying quantum mechanics … . The aim of Jan-Markus Schwindt is, in one hand, to make a standard material vivid, clear and interesting, on the other hand, to expand horizons going beyond the standard topics and outlining connections between different subjects. … The book is easy and pleasant to read.” (Yana Kinderknecht, zbMATH, Vol. 1286, 2014)Table of ContentsI Formalismus und Interpretation.- 1 Einleitung: Nichtlokal oder unreal?.- 2 Formalismus I: Endlichdimensionale Hilbert-Räume.- 3 Formalismus II: Unendlichdimensionale Hilbert-Räume.- 4 Interpretationen.- II Einzelnes skalares Teilchen in äußerem Potenzial.- 5 Eindimensionale Probleme.- 6 Zweidimensionale Systeme.- 7 Dreidimensionale Systeme.- 8 Streutheorie.- III Weiterführende Themen.- 9 Spin.- 10 Elektromagnetische Wechselwirkung.- 11 Störungstheorie.- 12 N-Teilchen-Systeme.- 13 Pfadintegral.- 14 Dirac-Gleichung.- 15 Quanten-Pandämonium.- Lösungen der Aufgaben.- Literaturverzeichnis.- Index.

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Book SynopsisThis book compactly provides the fundamentals of experimental physics for students of the natural sciences who are taking physics as a minor or major subject. Interspersed throughout the main text are numerous exercises with pre-calculated solutions, and the most important formulas are listed again at the end of each chapter. This book enables readers to gain an overview of the individual areas and is thus ideally suited to accompany lectures during studies as well as for exam preparation.The textbook originated from a lecture on "Experimental Physics for Natural Scientists" at the University of Tübingen and is intended for all students in subjects such as biochemistry, bioinformatics, biology, chemistry, computer science, mathematics, pharmacy, geoecology, and earth sciences.The first part of the book deals with Newtonian mechanics including continuum mechanics and oscillations and waves. The second part deals with the basic concepts of thermodynamics with emphasis on the statistical explanations. The third part covers electromagnetic phenomena, especially electrostatics and magnetostatics, electrodynamics, and an introduction to electronic components and circuits. Optics with its subfields, ray optics, wave optics, and quantum optics, is presented in the fourth part. In the fifth and last part of the book, the reader is given an overview of the basic principles of quantum mechanics, including atomic and nuclear physics. For this second edition, the content has been improved and supplemented in many places, including a new section on heat transport and phase transitions, as well as an outlook into alternative interpretations of quantum mechanics. Table of ContentsPhysical quantities and measurements.- Mechanics of rigid bodies.- Continuum mechanics.- Oscillations and waves.- Thermodynamics.- Electrostatics.- Magnetostatics.- Electrodynamics.- Electronics.- Optics.- Fundamentals of quantum physics.

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Book SynopsisDieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

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Book SynopsisThe first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.Trade Review“QM has also been the source of many interesting mathematical problems and developments to which only very few books devote careful attention and discussion. One of the praiseworthy merits of Dell'Antonio's book is to present a comprehensive and updates account of such important mathematical results. … For these reasons the book qualifies as a must for the education of mathematical physics graduate students and clearly provides very useful information also for theoretical physicists as well for mathematicians.” (Franco Strocchi, zbMATH 1357.81001, 2017)“This is a huge book on the mathematical foundations of quantum theory, including both non-relativistic quantum mechanics (QM) and quantum field theories (QFT). … the specialized reader will find in the book a very nice reference for checking concepts and ways of proceedings in these domains. It is a remarkable book.” (Décio Krause, Mathematical Reviews, May, 2016)Table of ContentsElements of the history of Quantum Mechanics I.- Elements of the history of Quantum Mechanics II.- Axioms, states, observables, measurement, difficulties.- Entanglement, decoherence, Bell’s inequalities, alternative theories.- Automorphisms; Quantum dynamics; Theorems of Wigner, Kadison, Segal; Continuity andgenerators.- Operators on Hilbert spaces I; Basic elements.- Quadratic forms.- Properties of free motion, Anholonomy,Geometric phase.- Elements of C ∗-algebras, GNS representation,automorphisms and dynamical systems.- Derivations and generators. K.M.S. condition. Elements of modular structure. Standard form.- Semigroups and dissipations. Markov approximation.- Quantum dynamical semigroups I.- Positivity preserving contraction semigroups on C ∗-algebras.- Conditional expectations.- Complete Dissipations.- Weyl system, Weyl algebra, lifting symplectic maps.- Magnetic Weyl algebra.- A Theorem of Segal.- Representations of Bargmann, Segal, Fock.- Second quantization.- Other quantizations (deformation, geometric).

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Book SynopsisThis book presents state-of-the-art research on quantum hybridization, manipulation, and measurement in the context of hybrid quantum systems. It covers a broad range of experimental and theoretical topics relevant to quantum hybridization, manipulation, and measurement technologies, including a magnetic field sensor based on spin qubits in diamond NV centers, coherently coupled superconductor qubits, novel coherent couplings between electron and nuclear spin, photons and phonons, and coherent coupling of atoms and photons. Each topic is concisely described by an expert at the forefront of the field, helping readers quickly catch up on the latest advances in fundamental sciences and technologies of hybrid quantum systems, while also providing an essential overview.Table of ContentsChapter 1: Quantum hybrid sensor by NV centers in diamond Authored by Norikazu MIZUOCHI Chapter 2: Magnetic Field Sensing using Nitrogen-Vacancy Centers in Diamond Authored by Junko Ishi-Hayase and Yuichiro Matsuzaki Chapter 3: Wide-field imaging using ensembles of NV centers in diamond Authored by Shintaro Nomura Chapter 4: Collective behaviour in hybrid quantum systems Authored by Yusuke Hama, Andreas Angerer, Emi Yukawa, W. J. Munro and Kae Nemoto Chapter 5: Rare earth “non-spin-bath” crystals for hybrid quantum coupling Authored by Takehiko Tawara Chapter 6: Electron spin resonances detected by superconducting circuits Authored by Rangga P. Budoyo, Hiraku Toida, Shiro Saito Chapter 7: Quantum information and technologies with spin-based hybrid systems Authored by Yuimaru Kubo Chapter 8: Spins in silicon field-effect transistors Authored by Keiji Ono Chapter 9: Ge/Si core-shell nanowires for hybrid quantum systems Authored by Rui Wang, Jian Sun, Russell S. Deacon and Koji Ishibashi Chapter 10: Photonic quantum interfaces among different physical systems Authored by Rikizo Ikuta, Motoki Asano, Sahin K. Ozdemir, Takashi Yamamoto Chapter 11: Hybrid quantum system of photons and nuclear spins of fermionic neutral atoms in a tunable optical lattice Authored by Hideki Ozawa, Shintaro Taie, Yosuke Takasu, and Yoshiro Takahashi Chapter 12: Phonon-electron-nuclear spin hybrid systems in an electromechanical resonator Authored by Yuma Okazaki and Hiroshi Yamaguchi Chapter 13: Cavity Quantum Electrodynamics with Laser-Cooled Atoms and Optical Nanofibers Authored by Takao Aoki Chapter 14: Robust quantum sensing Authored by Yuichiro Matsuzaki Chapter 15: Transferring quantum information in hybrid quantum systems consisting of a quantum system with limited control and a quantum computer Authored by Ryosuke Sakai, Akihito Soeda, Mio Murao

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Book SynopsisThis book highlights the importance of Electron Statistics (ES), which occupies a singular position in the arena of solid state sciences, in heavily doped (HD) nanostructures by applying Heisenberg’s Uncertainty Principle directly without using the complicated Density-of-States function approach as given in the literature. The materials considered are HD quantum confined nonlinear optical, III-V, II-VI, IV-VI, GaP, Ge, PtSb2, stressed materials, GaSb, Te, II-V, Bi2Te3, lead germanium telluride, zinc and cadmium diphosphides, and quantum confined III-V, IV-VI, II-VI and HgTe/CdTe super-lattices with graded interfaces and effective mass super-lattices. The presence of intense light waves in optoelectronics and strong electric field in nano-devices change the band structure of materials in fundamental ways, which have also been incorporated in the study of ES in HD quantized structures of optoelectronic compounds that control the studies of the HD quantum effect devices under strong fields. The influence of magnetic quantization, magneto size quantization, quantum wells, wires and dots, crossed electric and quantizing fields, intense electric field, and light waves on the ES in HD quantized structures and superlattices are discussed. The content of this book finds six different applications in the arena of nano-science and nanotechnology and the various ES dependent electronic quantities, namely the effective mass, the screening length, the Einstein relation and the elastic constants have been investigated. This book is useful for researchers, engineers and professionals in the fields of Applied Sciences, solid state and materials science, nano-science and technology, condensed matter physics, and allied fields, including courses in semiconductor nanostructures. ​Table of ContentsPlease see Attachments tab for detailed ToC​

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