Classical and Quantum Dynamics

by Dittrich, Walter; Reuter, Martin

• ISBN13: 9783540420668
• ISBN10: 3540420665
• Edition: 3rd
• Format: Paperback
• Copyright: 2001-08-01
• Publisher: Springer Verlag

Summary

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 new edition has been revised and enlarged with chapters on the action principle in classical electrodynamics, on the functional derivative approach, and on computing traces.

Table of Contents

Introduction	1	(2)
The Action Principles in Mechanics	3	(12)
The Action Principle in Classical Electrodynamics	15	(6)
Application of the Action Principles	21	(20)
Jacobi Fields, Conjugate Points	41	(12)
Canonical Transformations	53	(14)
The Hamilton---Jacobi Equation	67	(16)
Action-Angle Variables	83	(22)
The Adiabatic Invariance of the Action Variables	105	(12)
Time-Independent Canonical Perturbation Theory	117	(8)
Canonical Perturbation Theory with Several Degrees of Freedom	125	(14)
Canonical Adiabatic Theory	139	(6)
Removal of Resonances	145	(10)
Superconvergent Perturbation Theory, KAM Theorem (Introduction)	155	(8)
Poincare Surface of Sections, Mappings	163	(10)
The KAM Theorem	173	(8)
Fundamental Principles of Quantum Mechanics	181	(6)
Functional Derivative Approach	187	(10)
Examples for Calculating Path Integrals	197	(20)
Direct Evaluation of Path Integrals	217	(10)
Linear Oscillator with Time-Dependent Frequency	227	(16)
Propagators for Particles in an External Magnetic Field	243	(6)
Simple Applications of Propagator Functions	249	(16)
The WKB Approximation	265	(10)
Computing the Trace	275	(6)
Partition Function for the Harmonic Oscillator	281	(6)
Introduction to Homotopy Theory	287	(6)
Classical Chern---Simons Mechanics	293	(12)
Semiclassical Quantization	305	(6)
The ``Maslov Anomaly'' for the Harmonic Oscillator	311	(8)
Maslov Anomaly and the Morse Index Theorem	319	(6)
Berry's Phase	325	(16)
Classical Analogues to Berry's Phase	341	(16)
Berry Phase and Parametric Harmonic Oscillator	357	(14)
Topological Phases in Planar Electrodynamics	371	(10)
References	381	(2)
Index	383