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Saturday, May 2, 2020 | History

4 edition of Asymptotic methods for wave and quantum problems found in the catalog.

Asymptotic methods for wave and quantum problems

  • 159 Want to read
  • 16 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Differential equations, Nonlinear -- Asymptotic theory.,
  • Nonlinear waves -- Mathematics.,
  • Quantum theory -- Mathematics.,
  • Mathematical physics.

  • Edition Notes

    Includes bibliographical references.

    StatementM.V. Karasev, editor.
    SeriesAmerican Mathematical Society translations,, ser. 2, v. 208, Advances in the mathematical sciences ;, 53
    ContributionsKarasev, M. V.
    Classifications
    LC ClassificationsQA3 .A572 ser. 2, vol. 208
    The Physical Object
    Paginationviii, 284 p. :
    Number of Pages284
    ID Numbers
    Open LibraryOL3433253M
    ISBN 100821833367
    LC Control Number2005272130
    OCLC/WorldCa51979884

    Since the preparation of the first edition, there have been no changes in the fundamental ideas underlying the first 48 sections of the book, which deal with the quantum mechanics of particles and linear wave fields. This is not true of the last two sections, which are an introduction to the quantum mechanics of interacting wave Rating: % positive. Share. About this book.

    @article{osti_, title = {Class of model problems in three-body quantum mechanics that admit exact solutions}, author = {Takibayev, N. Zh., E-mail: [email protected]}, abstractNote = {An approach to solving scattering problems in three-body systems for cases where the mass of one of the particles is extremely small in relation to the masses of the other two particles and where the pair.   () Asymptotic Eigenvalue Distribution for the Wave Equation in a Cylinder of Arbitrary Cross Section. Physical Review A , () Progress in Weyl's problem achieved by computational by:

    Lecture 3: Asymptotic Methods for the Reduced Wave Equation Joseph B. Keller 1 The Reduced Wave Equation When n(X) is constant, the reduced wave equation has the plane wave solution u(X,K) = z(K)einKX. (6) We are interested in looking at the asymptotic behavior of solutions to the reduced wave equation (5) as k → ∞. To explore. The volume is suitable for graduate students and researchers interested in mathematical physics. Other AMS publications by M. Karasev include Nonlinear Poisson Brackets. Geometry and Quantization, Coherent Transform, Quantization, and Poisson Geometry, and Asymptotic Methods for Wave and Quantum Problems.


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Asymptotic methods for wave and quantum problems Download PDF EPUB FB2

Contains four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. This collection discusses applications of asymptotic methods to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations.

Asymptotic Methods for Wave and Quantum Problems by N. Uraltseva,available at Book Depository with free delivery worldwide. The collection consists of Asymptotic methods for wave and quantum problems book papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used.

The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of. Asymptotic methods in nonlinear wave phenomena in honor of the 65th birthday of Antonio Greco, Palermo, Italy, June / Published: () Asymptotic methods for relaxation oscillations and applications / by: Grasman, Johan.

Published: (). Asymptotic Wave Theory investigates the asymptotic behavior of wave representations and presents some typical results borrowed from hydrodynamics and elasticity theory.

It describes techniques such as Fourier-Laplace transforms, operational calculus, Book Edition: 1. Asymptotic Methods in Quantum Mechanics is a detailed discussion of the general properties of the wave functions of many particle systems. Particular emphasis is placed on their asymptotic behaviour, since the outer region of the wave function is most sensitive to external interaction.

Buy Short-Wavelength Diffraction Theory: Asymptotic Methods (Springer Series on Wave Phenomena (4)) on FREE SHIPPING on qualified ordersCited by: The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.

The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in.

Let us proceed to discuss the essentials of an asymptotic methods applied to the different limit of closely spaced disks by other authors. Consider the case of a square array and introduce the dimensionless gap parameter δ = 1 − 2 r r where 1 – 2r is the distance between the neighboring disks of radius gap parameter can be expressed through the concentration f as δ = π f − 2.

This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods. The short wavelength or high frequency asymptotic theory of the reduced wave equation and of Maxwell’s equations is presented.

The theory is applied to representative problems involving reflection, transmission, and diffraction in both homogeneous and inhomogeneous media. It is a slightly revised version of a report 1 written in by the Cited by: Guiding, Diffraction, and Confinement of Optical Radiation presents a wide array of research studies on optics and electromagnetism.

This book is organized into eight chapters that cover the problems related to optical radiation propagation and confinement. Chapter II is devoted to asymptotic methods of solution of the wave equation, with.

Numerical methods for quantum systems; A collection of problems at the end of each chapter develops students’ understanding of both basic concepts and the application of theory to various physically important systems.

This book, along with the authors’ follow-up Quantum Mechanics II: Advanced Topics, provides students with a broad, up-to. Quantum mechanics is the study of the behaviour of matter and energy at the molecular, atomic, nuclear levels and even at sub-nuclear level.

This book is intended to provide a broad introduction. In these notes we will focus on methods for the construction of asymptotic solutions, and we will not discuss in detail the existence of solutions close to the asymptotic solution.

Regular and singular perturbation problems It is useful to make an imprecise distinction between regular perturbation problems and singular perturbation problems. Short-Wavelength Diffraction Theory book. Read reviews from world’s largest community for readers. In the study of short-wave diffraction problems, asymp Ratings: 0.

Asymptotic safety (sometimes also referred to as nonperturbative renormalizability) is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and.

Approach to Equilibrium and Related Problems in Quantum Systems with an Infinite Number of Degrees of Freedom. Quantum mixing, dynamical stability, return to equilibrium and weak asymptotic abelianness; Examples of mixing and weak asymptotic abelianness: The.

Asymptotic Methods for Integrable Systems in Nonlinear Wave Theory Ap Introduction But we are not finished. Information must be extracted from the integrals. Classical tools for asymptotic analysis of integrals: • Laplace’s method.

• Method of steepest descent. • Method of stationary phase. This volume is concerned with a detailed description of the canonical operator method - one of the asymptotic methods of linear mathematical physics. The book is, in fact, an extension and continuation of the authors' works [59], [60], [65].

The basic ideas are summarized in the Introduction. The book consists of two parts. In the first, the theory of the canonical operator is develop ed.This is a reprinting of a book originally published in At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic : Leonard Eisenbud.For a large class of interactions the existence of the asymptotic velocity and the asymptotic completeness of the wave operators is shown.

The book is self-contained and explains in detail concepts that deepen the understanding. As a special feature of the book, the beautiful analogy between classical and quantum scattering theory (e.g., for N.