Ebook: The Complex WKB Method for Nonlinear Equations I: Linear Theory

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 The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian.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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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 The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian.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 Schr?dinger 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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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 The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian.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 Schr?dinger 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.
Content:
Front Matter....Pages i-vii
Introduction....Pages 1-5
Equations and Problems of Narrow Beam Mechanics....Pages 7-29
Hamiltonian Formalism of Narrow Beams....Pages 31-67
Approximate Solutions of the Nonstationary Transport Equation....Pages 69-110
Stationary Hamilton-Jacobi and Transport Equations....Pages 111-153
Complex Hamiltonian Formalism of Compact (CYCLIC) Beams....Pages 155-200
Canonical Operators on Lagrangian Manifolds with Complex Germ and their Applications to Spectral Problems of Quantum Mechanics....Pages 201-250
Back Matter....Pages 251-302

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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 Schr?dinger 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.
Content:
Front Matter....Pages i-vii
Introduction....Pages 1-5
Equations and Problems of Narrow Beam Mechanics....Pages 7-29
Hamiltonian Formalism of Narrow Beams....Pages 31-67
Approximate Solutions of the Nonstationary Transport Equation....Pages 69-110
Stationary Hamilton-Jacobi and Transport Equations....Pages 111-153
Complex Hamiltonian Formalism of Compact (CYCLIC) Beams....Pages 155-200
Canonical Operators on Lagrangian Manifolds with Complex Germ and their Applications to Spectral Problems of Quantum Mechanics....Pages 201-250
Back Matter....Pages 251-302
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