Description
Book SynopsisQuantum mechanics is vitally important in the study and design of semiconductor devices and in the emerging field of quantum computing. Whereas most quantum mechanics books are written for a physics audience, this book is aimed at electrical engineers and materials scientists.
Table of ContentsIntroduction.
PART I: FOUNDATIONS.
1. Particles and Waves.
2. Probability Amplitudes.
3. The Origins of Quantum Mechanics.
4. The Schrödinger Equation and Wave Packet Solutions.
5. Operators, Expectation Values, and Ehrenfest's Theorem.
PART II: THE TIME-INDEPENDENT SCHRÖDINGER EQUATION.
6. Eigenfunctions and Eigenvalues.
7. Piecewise Constant Potentials: I.
8. Piecewise Constant Potentials: II.
PART III: THE SIMPLE HARMONIC OSCILLATOR.
9. The Simple Harmonic Oscillator I.
10. The Simple Harmonic Oscillator II: Operators.
11. The Simple Harmonic Oscillator III: Wave Packet Solutions.
12. The Quantum LC Circuit.
PART IV: USEFUL APPROXIMATIONS.
13. Overview of Approximate Methods for Eigenfunctions.
14. The WKB Approximation.
15. The Variational Method.
16. Finite Basis Approximation.
PART V: THE TWO-LEVEL SYSTEM.
17. The Two-level System with Static Coupling.
18. Th e Two-level System with Dynamical Coupling.
19. Coupld Two-level System and Simple Harmonic Oscillator.
PART VI: QUANTUM SYSTEMS WITH MANY DEGREES OF FREEDOM.
20. Problems in More than One Dimension.
21. Electromagnetic Field Quantization I: Resonator Fields.
22. Electromagnetic Field Quantization II: Free-space Fields.
23. The Density of States.
24. The Golden Rules: The Calculation of Transition Raes.
PART VII: STATISTICAL MECHANICS.
25. Basic Concepts of Statistical Mechanics.
26. Microscopic Quantum Systems in Equilibrium with a Reservoir.
27. Statistical Models Applied to Metals and Semiconductors.
PART VIII: HYDROGEN ATOM, HELIUM ATOM, AND MOLECULAR HYDROGEN.
28. The Hydrogen Atom I: The Classical Problems.
29. The Hydrogen Atom II: The Quantum Problem.
30. The Hydrogen Atom III: Applications.
31. Two-Electron Atoms and Ions.
32. Molecular Hydrogen I: H2+ and H2 Electronic Orbitals.
33. Molecular Hydrogen II: Vibrational and Rotational States.
PART IX: APPENDICES.
Appendix A: Gaussian Integrals.
Appendix B: The Fourier Transform of a Plane Wave.
Appendix C: The Probability Flux.
Appendix D: The Cascaded Matrix Method.
Appendix E: The Creation Operator Raises the Index.
Appendix F: Canonical Quantization.
Appendix G: Wave Packet Incident on a "Gentle" Potential Step.
Appendix H: The WKB Representation for Allowed Regions.
Appendix I: The WKB Representation for Forbidden Regions.
Appendix J: Matrix Elements for the Quartic Well.
Appendix K: Normalization, and the Unity Operator.
Appendix L: The Density Operator and Density Matrix.
Appendix M: The Two-level System Hamiltonian.
Appendix N: Thinking about Dirac Notation.
Appendix O: Coordinate Rotation and the Two-dimensional SHO.
Appendix P: Conservation Law for the Electromagnetic Energy Density.
Appendix Q: The Grand Partition Function.
Appendix R: Analytic Results for Metals Properties.
Appendix S: Saha Equilibrium for a Hydrogen Plasma.
Appendix T: Nuclear Magnetic Resonance.
Appendix U: The Atomic Force Microscope.
Appendix V: The Heisenberg Picture.
References.
Index.
