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Scattering Theory: Some Old and New Problems

  • Authors
  • Dmitri R. Yafaev

Part of the Lecture Notes in Mathematics book series (LNM, volume 1735)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Dmitri R. Yafaev
    Pages 1-13
  3. Dmitri R. Yafaev
    Pages 24-29
  4. Dmitri R. Yafaev
    Pages 40-46
  5. Dmitri R. Yafaev
    Pages 47-52
  6. Dmitri R. Yafaev
    Pages 53-58
  7. Dmitri R. Yafaev
    Pages 59-66
  8. Dmitri R. Yafaev
    Pages 67-79
  9. Dmitri R. Yafaev
    Pages 80-85
  10. Dmitri R. Yafaev
    Pages 86-95
  11. Dmitri R. Yafaev
    Pages 96-105
  12. Dmitri R. Yafaev
    Pages 106-117
  13. Dmitri R. Yafaev
    Pages 128-136
  14. Dmitri R. Yafaev
    Pages 137-144
  15. Dmitri R. Yafaev
    Pages 145-153
  16. Back Matter
    Pages 155-169

About this book

Introduction

Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.

Keywords

Fourier transform Wave operators asymptotic completeness long-range potentials n-body problem scattering matrix scattering theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0105531
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-67587-7
  • Online ISBN 978-3-540-45170-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site