Introductory Applied Quantum and Statistical Mechanics

Peter L. Hagelstein  is an Associate Professor in the Department of Electrical Engineering and Computer Science at M.I.T. He  is a principal investigator in the Optics and Quantum Electronics Group of the Research Laboratory of Electronics. Stephen D. Senturia joined the Department of Electrical Engineering and Computer Science at M.I.T. immediately after completing his education (MIT, Ph.D. in Physics, 1966), initially as Research Scientist, then as Assistant Professor in 1967, with subsequent promotions up the ranks. From 1992 to 2002, he held the Barton L. Weller Chair in Electrical Engineering. He has been involved in microsensor and MEMS research since the early 1970’s. For a number of years, his research focused on developing material-property measurement methods and CAD tools for MEMS. The work on MEMCAD led to the spin-out from his group of the two companies that lead this commercial field: IntelliSense and Coventor.He serves as Senior Editor of the ASME/IEEE Journal of Microelectromechanical Systems. After officially retiring from MIT in June, 2002, Dr. Senturia now has part-time duties at MIT and serves as Chairman and Chief Technology Officer of Polychromix, Inc., Woburn, MA, a company he founded to adapt the Polychromator technology for commercial use. Honor and professional societies include the IEEE (Fellow), Phi Beta Kappa, and Sigma Xi. Terry P. Orlando is a Professor at the Research Laboratory of Electronics at M.I.T. His research focuses on superconducting circuits for quantum computation and nonlinear dynamics.

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.