The Complex WKB Method for Nonlinear Equations I: Linear Theory: 16 (Progress in Mathematical Physics, 16) - Hardcover
Synopsis
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 The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian.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.
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Synopsis
The central mathematical idea of this text is to use topological methods to analyze isotropic invariant manifolds in order to obtain asymptotic series of eigenvalues and eigenvectors for the multi-dimensional Schroedinger 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), are considered in the second volume.
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Complex Wkb Method for Nonlinear Equations I : Linear Theory
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The complex WKB method for nonlinear equations. Progress in physics; Bd. 16.
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The Complex WKB Method for Nonlinear Equations I: Linear Theory (Progress in Mathematical Physics, 16)
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The Complex WKB Method for Nonlinear Equations I
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Springer, Basel, Birkhäuser Basel, Birkhäuser Aug 1994, 1994
ISBN 10: 3764350881
ISBN 13: 9783764350888
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book deals with asymptotic solutions of linear and nonlinear equa tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ o. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob lems of mathematical physics; certain specific formulas were obtained by differ ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: 'One can hope that in the near future a computational pro cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed. 304 pp. Englisch. Seller Inventory # 9783764350888
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The Complex WKB Method for Nonlinear Equations I: Linear Theory (Progress in Mathematical Physics, Band 16)
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Basel [u.a.]: Birkhäuser Verlag, 1994
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The Complex WKB Method for Nonlinear Equations I: Linear Theory (Progress in Physics, 16, Band 16)
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Complex Wkb Method for Nonlinear Equations I : Linear Theory
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The Complex WKB Method for Nonlinear Equations I: Linear Theory (Progress in Mathematical Physics) (v. 1)
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Condition: New. Includes examples of applications to physics. This title uses topological methods to analyze isotropic invariant manifolds in order to obtain asymptotic series of eigenvalues and eigenvectors for the multi-dimensional Schrodinger equation, and also takes into account the so-called tunnel effects. It reviews finite-dimensional linear theory. Translator(s): Shishkova, M.A.; Sossinsky, A. B. Series: Progress in Mathematical Physics. Num Pages: 304 pages, biography. BIC Classification: PBKD; PBKJ; PBM; PBP; PBW. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 166 x 242 x 25. Weight in Grams: 628. . 1994. 1994th Edition. Hardcover. . . . . Seller Inventory # V9783764350888