Introductory Applied Quantum and Statistical Mechanics

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.