The Complex Wkb Method For Nonlinear Equations
DOWNLOAD
Download The Complex Wkb Method For Nonlinear Equations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Complex Wkb Method For Nonlinear Equations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Complex Wkb Method For Nonlinear Equations I
DOWNLOAD
Author : Victor P. Maslov
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-08-01
The Complex Wkb Method For Nonlinear Equations I written by Victor P. Maslov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-08-01 with Science categories.
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.
The Complex Wkb Method For Nonlinear Equations I
DOWNLOAD
Author : Victor P. Maslov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Complex Wkb Method For Nonlinear Equations I written by Victor P. Maslov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
The Complex Wkb Method For Nonlinear Equations
DOWNLOAD
Author : Viktor P. Maslov
language : en
Publisher:
Release Date : 1994
The Complex Wkb Method For Nonlinear Equations written by Viktor P. Maslov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
The Complex Wkb Method For Nonlinear Equations I
DOWNLOAD
Author : V. P. Maslov
language : en
Publisher: Birkhauser
Release Date : 1994
The Complex Wkb Method For Nonlinear Equations I written by V. P. Maslov and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
Mathematical Modelling Of Heat And Mass Transfer Processes
DOWNLOAD
Author : V.G. Danilov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Modelling Of Heat And Mass Transfer Processes written by V.G. Danilov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In the present book the reader will find a review of methods for constructing a certain class of asymptotic solutions, which we call self-stabilizing solutions. This class includes solitons, kinks, traveling waves, etc. It can be said that either the solutions from this class or their derivatives are localized in the neighborhood of a certain curve or surface. For the present edition, the book published in Moscow by the Nauka publishing house in 1987, was almost completely revised, essentially up-dated, and shows our present understanding of the problems considered. The new results, obtained by the authors after the Russian edition was published, are referred to in footnotes. As before, the book can be divided into two parts: the methods for constructing asymptotic solutions ( Chapters I-V) and the application of these methods to some concrete problems (Chapters VI-VII). In Appendix a method for justification some asymptotic solutions is discussed briefly. The final formulas for the asymptotic solutions are given in the form of theorems. These theorems are unusual in form, since they present the results of calculations. The authors hope that the book will be useful to specialists both in differential equations and in the mathematical modeling of physical and chemical processes. The authors express their gratitude to Professor M. Hazewinkel for his attention to this work and his support.
Asymptotic Combinatorics With Application To Mathematical Physics
DOWNLOAD
Author : V.A. Malyshev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Combinatorics With Application To Mathematical Physics written by V.A. Malyshev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Mathematical Topics Between Classical And Quantum Mechanics
DOWNLOAD
Author : Nicholas P. Landsman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Topics Between Classical And Quantum Mechanics written by Nicholas P. Landsman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Subject Matter The original title of this book was Tractatus Classico-Quantummechanicus, but it was pointed out to the author that this was rather grandiloquent. In any case, the book discusses certain topics in the interface between classical and quantum mechanics. Mathematically, one looks for similarities between Poisson algebras and symplectic geometry on the classical side, and operator algebras and Hilbert spaces on the quantum side. Physically, one tries to understand how a given quan tum system is related to its alleged classical counterpart (the classical limit), and vice versa (quantization). This monograph draws on two traditions: The algebraic formulation of quan tum mechanics and quantum field theory, and the geometric theory of classical mechanics. Since the former includes the geometry of state spaces, and even at the operator-algebraic level more and more submerges itself into noncommutative geometry, while the latter is formally part of the theory of Poisson algebras, one should take the words "algebraic" and "geometric" with a grain of salt! There are three central themes. The first is the relation between constructions involving observables on one side, and pure states on the other. Thus the reader will find a unified treatment of certain aspects of the theory of Poisson algebras, oper ator algebras, and their state spaces, which is based on this relationship.
Quantum Mechanics
DOWNLOAD
Author : Gennaro Auletta
language : en
Publisher: Cambridge University Press
Release Date : 2009-04-16
Quantum Mechanics written by Gennaro Auletta and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-16 with Science categories.
The important changes quantum mechanics has undergone in recent years are reflected in this approach for students. A strong narrative and over 300 worked problems lead the student from experiment, through general principles of the theory, to modern applications. Stepping through results allows students to gain a thorough understanding. Starting with basic quantum mechanics, the book moves on to more advanced theory, followed by applications, perturbation methods and special fields, and ending with developments in the field. Historical, mathematical and philosophical boxes guide the student through the theory. Unique to this textbook are chapters on measurement and quantum optics, both at the forefront of current research. Advanced undergraduate and graduate students will benefit from this perspective on the fundamental physical paradigm and its applications. Online resources including solutions to selected problems, and 200 figures, with colour versions of some figures, are available at www.cambridge.org/Auletta.
The Einstein Equations And The Large Scale Behavior Of Gravitational Fields
DOWNLOAD
Author : Piotr T. Chruściel
language : en
Publisher: Springer Science & Business Media
Release Date : 2004
The Einstein Equations And The Large Scale Behavior Of Gravitational Fields written by Piotr T. Chruściel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
Accompanying DVD-ROM contains the electronic proceedings of the summer school on mathematical general relativity and global properties of solutions of Einstein's equations held at Cargèse, Corsica, France, July 20-Aug. 10, 2002.
Singular Perturbations I
DOWNLOAD
Author : L.S. Frank
language : en
Publisher: Elsevier
Release Date : 1990-08-16
Singular Perturbations I written by L.S. Frank and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-16 with Mathematics categories.
Singular perturbations, one of the central topics in asymptotic analysis, also play a special role in describing physical phenomena such as the propagation of waves in media in the presence of small energy dissipations or dispersions, the appearance of boundary or interior layers in fluid and gas dynamics, as well as in elasticity theory, semi-classical asymptotic approximations in quantum mechanics etc. Elliptic and coercive singular perturbations are of special interest for the asymptotic solution of problems which are characterized by boundary layer phenomena, e.g. the theory of thin buckling plates, elastic rods and beams. This first volume deals with linear singular perturbations (on smooth manifolds without boundary) considered as equicontinuous linear mappings between corresponding families of Sobolev-Slobodetski's type spaces of vectorial order.