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Introductory Applied Quantum and Statistical Mechanics

ISBN: 978-0-471-20276-9
785 pages
March 2004
Introductory Applied Quantum and Statistical Mechanics (0471202762) cover image
* An applied focus for electrical engineers and materials scientists.
* Theoretical results supported with real-world systems and applications.
* Includes worked examples and self-study questions.
* Solutions manual available.
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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.

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PETER L. HAGELSTEIN is an associate professor in the Department of Electrical Engineering and Computer Science at MIT. He is a principal investigator in the Optics and Quantum Electronics Group of the Research Laboratory of Electronics.
STEPHEN D. SENTURIA formerly held the Barton L. Weller Chair in Electrical Engineering at MIT. He retired in 2002, and currently serves as Chairman and Chief Technology Officer of Polychromix, Inc. in Woburn, Massachusetts. He is Senior Editor of the ASME/IEEE Journal of Microelectromechanical Systems.
TERRY P. ORLANDO is a professor of electrical engineering and principal investigator at the Research Laboratory of Electronics at MIT. His research focuses on superconducting circuits for quantum computation and nonlinear dynamics.
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