Introductory Applied Quantum and Statistical Mechanics

Introduction. 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.