Chaos in Classical and Quantum Mechanics

✍ Scribed by Martin C. Gutzwiller (auth.)

Publisher: Springer-Verlag New York
Year: 1990
Tongue: English
Leaves: 445
Series: Interdisciplinary Applied Mathematics 1
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.

✦ Table of Contents

Front Matter....Pages i-xiii
Introduction....Pages 1-4
The Mechanics of Lagrange....Pages 5-18
The Mechanics of Hamilton and Jacobi....Pages 19-29
Integrable Systems....Pages 30-44
The Three-Body Problem: Moon — Earth — Sun....Pages 45-57
Three Methods of Solution....Pages 58-74
Periodic Orbits....Pages 75-86
The Surface of Section....Pages 87-98
Models of the Galaxy and of Small Molecules....Pages 99-115
Soft Chaos and the KAM Theorem....Pages 116-141
Entropy and Other Measures of Chaos....Pages 142-155
The Anisotropic Kepler Problem....Pages 156-172
The Transition from Classical to Quantum Mechanics....Pages 173-193
The New World of Quantum Mechanics....Pages 194-206
The Quantization of Integrable Systems....Pages 207-230
Wave Functions in Classically Chaotic Systems....Pages 231-253
The Energy Spectrum of a Classically Chaotic System....Pages 254-281
The Trace Formula....Pages 282-321
The Diamagnetic Kepler Problem....Pages 322-339
Motion on a Surface of Constant Negative Curvature....Pages 340-382
Scattering Problems, Coding, and Multifractal Invariant Measures....Pages 383-409
Back Matter....Pages 410-432