Chaos in Classical and Quantum Mechanics

by Martin C. Gutzwiller

Overview

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.

Product Details

ISBN-13:	9780387971735
Publisher:	Springer New York
Publication date:	10/23/1990
Series:	Interdisciplinary Applied Mathematics , #1
Edition description:	1990
Pages:	432
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

Contents: Introduction.- The Mechanics of Lagrange.- The Mechanics of Hamilton and Jacobi.- Integrable Systems.- The Three-Body Problem: Moon-Earth-Sun.- Three Methods of Section.- Periodic Orbits.- The Surface of Solution.- Models of the Galaxy and of Small Molecules.- Soft Chaos and the KAM Theorem.- Entropy and Other Measures of Chaos.- The Anisotropic Kepler Problem.- The Transition From Classical to Quantum Mechanics.- The New World of Quantum Mechanics.- The Quantization of Integrable Systems.- Wave Functions in Classically Chaotic Systems.- The Energy Spectrum of a Classically Chaotic System.- The Trace Formula.- The Diamagnetic Kepler Problem.- Motion on a Surface of Constant Negative Curvature.- Scattering Problems, Coding and Multifractal Invariant Measures.- References.- Index.

Editorial Reviews

Describes the apparent chaos in the long time-interval motions of simple mechanical systems for an audience at the level of beginning graduate students, developing the relevant ideas with the help of geometric intuition rather than algebraic manipulation. The main focus is on seeking the connection between classical and quantum mechanics. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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