Classical and Quantum Dynamics from Classical Paths to Path Integrals
In the past 10 to 15 years, the quantum leap in understanding of nonlinear dynamics has radically changed the frame of reference of physicists contemplating such systems. This book treats classical and quantum mechanics using an approach as introduced by nonlinear Hamiltonian dynamics and path integ...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1992, 1992
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| Edition: | 1st ed. 1992 |
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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. Time-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. Poincaré 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 Chern-Simons Mechanics
- 25. Semiclassical Quantization
- 26. The “Maslov Anomaly” for the Harmonic Oscillator
- 27. Maslov Anomaly and the Morse Index Theorem
- 28. Berry’s Phase
- 29. Classical Analogues to Berry’s Phase
- 30. Berry Phase and Parametric Harmonic Oscillator
- References