The Complex WKB Method for Nonlinear Equations I: Linear Theory / Edition 1

The Complex WKB Method for Nonlinear Equations I: Linear Theory / Edition 1

by Victor P. Maslov
     
 

ISBN-10: 3764350881

ISBN-13: 9783764350888

Pub. Date: 08/01/1994

Publisher: Birkhauser Basel

When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry; indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available

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Overview

When this book was first published (in Russian), it proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry; indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian. Its central mathematical idea is to use topological methods to analyze isotropic invariant manifolds in order to obtain asymptotic series of eigenvalues and eigenvectors for the multi-dimensional Schrödinger equation, and also to take into account the so-called tunnel effects. Finite-dimensional linear theory is reviewed in detail. Infinite-dimensional linear theory and its applications to quantum statistics and quantum field theory, as well as the nonlinear theory (involving instantons), will be considered in a second volume.

Product Details

ISBN-13:
9783764350888
Publisher:
Birkhauser Basel
Publication date:
08/01/1994
Series:
Progress in Mathematical Physics Series, #16
Edition description:
1994
Pages:
304
Product dimensions:
6.20(w) x 9.30(h) x 1.00(d)

Table of Contents

I. Equations and problems of narrow beam mechanics.- II. Hamiltonian formalism of narrow beams.- III. Approximate solutions of the nonstationary transport equation.- IV. Stationary Hamilton-Jacobi and transport equations.- V. Complex Hamiltonian formalism of compact (cyclic) beams.- VI. Canonical operators on Lagrangian manifolds with complex germ and their applications to spectral problems of quantum mechanics.- References.- Appendix A Complex germ generated by a linear connection.- Appendix B Asymptotic solutions with pure imaginary phase and the tunnel equation.- Appendix C Analytic asymptotics of oscillatory decreasing type (heuristic considerations).

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