Classical and Quantum Dynamics
from Classical Paths to Path Integrals
1st Edition
Published on 6. December 2012
VIII, 341 pages
978-3-642-97921-7 (ISBN)
Description
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 integral methods. It is written for
graduate students who want to become familiar with the more
advancedcomputational strategies in classical and quantum
dynamics. Therefore, worked examples comprise a large part
of the text. While the first half of the book lays the
groundwork for a standard course, the second half, with its
detailed treatment of the time-dependent oscillator,
classical and quantum Chern-Simons mechanics, the Maslov
anomaly and the Berry phase, willacquaint the reader with
modern topological methods that have not as yet found their
way into the textbook literature.
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Walter Dittrich | Martin Reuter
Classical and Quantum Dynamics
from Classical Paths to Path Integrals
E-Book
12/2012
2nd Edition
Springer
€82.38
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Additional editions
Walter Dittrich | Martin Reuter
Classical and Quantum Dynamics
from Classical Paths to Path Integrals
Book
04/1992
Springer
€85.55
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Content
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.
