Classical and Quantum Dynamics: from Classical Paths to Path Integrals

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

• Publisher: Springer Berlin Heidelberg
• Year: 1992
• Tongue: English
• Leaves: 332
• Edition: Softcover reprint of the original 1st ed. 1992
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-vii
Introduction....Pages 1-2
The Action Principles in Mechanics....Pages 3-14
Application of the Action Principles....Pages 15-33
Jacobi Fields, Conjugate Points....Pages 35-45
Canonical Transformations....Pages 47-60
The Hamilton-Jacobi Equation....Pages 61-73
Action-Angle Variables....Pages 75-96
The Adiabatic Invariance of the Action Variables....Pages 97-107
Time-Independent Canonical Perturbation Theory....Pages 109-115
Canonical Perturbation Theory with Several Degrees of Freedom....Pages 117-129
Canonical Adiabatic Theory....Pages 131-136
Removal of Resonances....Pages 137-145
Superconvergent Perturbation Theory, KAM Theorem (Introduction)....Pages 147-154
Poincaré Surface of Sections, Mappings....Pages 155-163
The KAM Theorem....Pages 165-171
Fundamental Principles of Quantum Mechanics....Pages 173-177
Examples for Calculating Path Integrals....Pages 179-198
Direct Evaluation of Path Integrals....Pages 199-208
Linear Oscillator with Time-Dependent Frequency....Pages 209-223
Propagators for Particles in an External Magnetic Field....Pages 225-229
Simple Applications of Propagator Functions....Pages 231-246
The WKB Approximation....Pages 247-256
Partition Function for the Harmonic Oscillator....Pages 257-262
Introduction to Homotopy Theory....Pages 263-267
Classical Chern-Simons Mechanics....Pages 269-279
Semiclassical Quantization....Pages 281-286
The “Maslov Anomaly” for the Harmonic Oscillator....Pages 287-294
Maslov Anomaly and the Morse Index Theorem....Pages 295-300
Berry’s Phase....Pages 301-309
Classical Analogues to Berry’s Phase....Pages 311-322
Berry Phase and Parametric Harmonic Oscillator....Pages 323-335
Back Matter....Pages 337-341

✦ Subjects

Statistical Physics, Dynamical Systems and Complexity;Quantum Physics;Quantum Information Technology, Spintronics