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经典和量子动力学 第2版 英文版 W.Dittrich，M.Reuter 著 1998年版
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经典和量子动力学 第2版 英文版
作者：W.Dittrich，M.Reuter 著
出版时间：1998年版
内容简介
This volume is the result of the authors' lectures and seminars given at Tiibingcn University and elsewhere. It represents a summary of our learning process in non-linear Hamiltonian dynamics and path integral methods in nonrelativistic quantum mechanics. While large parts of the book are based on standard material, readers will find numerous worked examples which can rarely be found in the published literature. In fact, toward the end they will find themselves in the midst of mod- em topological methods which so far have not made their way into the textbook literature.
One of the authors' (W.D.) interest in the subject was inspired by Prof. D. Judd (UC Berkeley), whose lectures on nonlinear dynamics familiarized him with Lich-tenberg and Lieberman's monograph, Regular and Stochastic Motion (Springer, 1983). For people working in plasma or accelerator physics, the chapter on non-linear physics should contain some familiar material. Another influential author has been Prof. J. Schwinger (UCLA); the knowledgeable reader will not be surprised to discover our appreciation of Schwinger's Action Principle in the introductory chapters. However, the major portion of the book is based on Feynman's path integral approach, which seems to be the proper language for handling topological aspects in quantum physics.
目 录
Introduction
1. The Action Principles in Mechanics
2. Application of the Action Principles
3. Jacobi Fields， Conjugate Points
4. Canonical Transformations
5. The Hamilton-Jacobi Equation
6. Action-Angle Variables
7. The Adiabatic Invariance of the Action Variables
8. Tune-Independent Canonical Perturbation Theory
9. Canonical Perturbation Theory with Several Degrees of Freedom
10. Canonical Adiabatic Theory
11. Removal of Resonances
12. Superconvergent Perturbation Theory， KAM Theorem (Introduction)
13. Poincare Surface of Sections， Mappings
14. The KAM Theorem
15. Fundamental Principles of Quantum Mechanics
16. Examples for Calculating Path Integrals
17. Direct Evaluation of Path Integrals
18. Linear Oscillator with Time-Dependent Frequency
19. Propagators for Particles in an External Magnetic Field
20. Simple Applications of Propagator Functions
21. The WKB Approximation
22. Partition Function for the Harmonic Oscillator
23. Introduction to Homotopy Theory
24. Classical Chem-Simons Mechanics
25. Semicalssical Quantization
26. The"Maslov Anomaly and the Morse Index Theorem
27. Maslov Anomaly and the Morse Index Theorem
28. Berry's Phase
29. Classical Analoues to Berry's Phase
30. Berry Phase and Parametric Harmonic Oscillator
31. Topological Phases in Planar Electrodynamics
References
Subject Index
作者：W.Dittrich，M.Reuter 著
出版时间：1998年版
内容简介
This volume is the result of the authors' lectures and seminars given at Tiibingcn University and elsewhere. It represents a summary of our learning process in non-linear Hamiltonian dynamics and path integral methods in nonrelativistic quantum mechanics. While large parts of the book are based on standard material, readers will find numerous worked examples which can rarely be found in the published literature. In fact, toward the end they will find themselves in the midst of mod- em topological methods which so far have not made their way into the textbook literature.
One of the authors' (W.D.) interest in the subject was inspired by Prof. D. Judd (UC Berkeley), whose lectures on nonlinear dynamics familiarized him with Lich-tenberg and Lieberman's monograph, Regular and Stochastic Motion (Springer, 1983). For people working in plasma or accelerator physics, the chapter on non-linear physics should contain some familiar material. Another influential author has been Prof. J. Schwinger (UCLA); the knowledgeable reader will not be surprised to discover our appreciation of Schwinger's Action Principle in the introductory chapters. However, the major portion of the book is based on Feynman's path integral approach, which seems to be the proper language for handling topological aspects in quantum physics.
目 录
Introduction
1. The Action Principles in Mechanics
2. Application of the Action Principles
3. Jacobi Fields， Conjugate Points
4. Canonical Transformations
5. The Hamilton-Jacobi Equation
6. Action-Angle Variables
7. The Adiabatic Invariance of the Action Variables
8. Tune-Independent Canonical Perturbation Theory
9. Canonical Perturbation Theory with Several Degrees of Freedom
10. Canonical Adiabatic Theory
11. Removal of Resonances
12. Superconvergent Perturbation Theory， KAM Theorem (Introduction)
13. Poincare Surface of Sections， Mappings
14. The KAM Theorem
15. Fundamental Principles of Quantum Mechanics
16. Examples for Calculating Path Integrals
17. Direct Evaluation of Path Integrals
18. Linear Oscillator with Time-Dependent Frequency
19. Propagators for Particles in an External Magnetic Field
20. Simple Applications of Propagator Functions
21. The WKB Approximation
22. Partition Function for the Harmonic Oscillator
23. Introduction to Homotopy Theory
24. Classical Chem-Simons Mechanics
25. Semicalssical Quantization
26. The"Maslov Anomaly and the Morse Index Theorem
27. Maslov Anomaly and the Morse Index Theorem
28. Berry's Phase
29. Classical Analoues to Berry's Phase
30. Berry Phase and Parametric Harmonic Oscillator
31. Topological Phases in Planar Electrodynamics
References
Subject Index
