Classical and Quantum Dynamics: From Classical Paths to Path Integrals

✍ Scribed by Prof. Dr. Walter Dittrich, Prof. Dr. Martin Reuter (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2001
• Tongue: English
• Leaves: 381
• Series: Advanced Texts in Physics
• Edition: 3
• Category: Library

✦ Synopsis

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

Front Matter....Pages I-X
Introduction....Pages 1-2
The Action Principles in Mechanics....Pages 3-14
The Action Principle in Classical Electrodynamics....Pages 15-19
Application of the Action Principles....Pages 21-40
Jacobi Fields, Conjugate Points....Pages 41-52
Canonical Transformations....Pages 53-66
The Hamilton—Jacobi Equation....Pages 67-82
Action-Angle Variables....Pages 83-104
The Adiabatic Invariance of the Action Variables....Pages 105-115
Time-Independent Canonical Perturbation Theory....Pages 117-123
Canonical Perturbation Theory with Several Degrees of Freedom....Pages 125-138
Canonical Adiabatic Theory....Pages 139-144
Removal of Resonances....Pages 145-153
Superconvergent Perturbation Theory, KAM Theorem (Introduction)....Pages 155-162
Poincaré Surface of Sections, Mappings....Pages 163-172
The KAM Theorem....Pages 173-179
Fundamental Principles of Quantum Mechanics....Pages 181-185
Functional Derivative Approach....Pages 187-196
Examples for Calculating Path Integrals....Pages 197-216
Direct Evaluation of Path Integrals....Pages 217-226
Linear Oscillator with Time-Dependent Frequency....Pages 227-241
Propagators for Particles in an External Magnetic Field....Pages 243-247
Simple Applications of Propagator Functions....Pages 249-264
The WKB Approximation....Pages 265-274
Computing the Trace....Pages 275-279
Partition Function for the Harmonic Oscillator....Pages 281-286
Introduction to Homotopy Theory....Pages 287-291
Classical Chern—Simons Mechanics....Pages 293-304
Semiclassical Quantization....Pages 305-310
The “Maslov Anomaly” for the Harmonic Oscillator....Pages 311-318
Maslov Anomaly and the Morse Index Theorem....Pages 319-324
Berry’s Phase....Pages 325-340
Classical Analogues to Berry’s Phase....Pages 341-356
Berry Phase and Parametric Harmonic Oscillator....Pages 357-369
Topological Phases in Planar Electrodynamics....Pages 371-379
Back Matter....Pages 381-385

✦ Subjects

Quantum Physics