UID:
almahu_9949199261702882
Format:
IX, 361 p.
,
online resource.
Edition:
2nd ed. 1994.
ISBN:
9783642974656
Content:
Graduate students who want to become familiar with advanced computational strategies in classical and quantum dynamics will find here both the fundamentals of a standard course and a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, together with many worked examples throughout the text. This second edition has been enlarged by a new chapter on topological phases in planar electrodynamics and a discussion of the Aharonov-Bohm effect.
Note:
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 -- 31. Topological Phases in Planar Electrodynamics -- References.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783540562450
Additional Edition:
Printed edition: ISBN 9783642974663
Language:
English
DOI:
10.1007/978-3-642-97465-6
URL:
https://doi.org/10.1007/978-3-642-97465-6
