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Mathematical Scattering Theory

  • Hellmut Baumgärtel
  • Manfred Wollenberg

Part of the Operator Theory: Advances and Applications book series (OT, volume 9)

Table of contents

  1. Front Matter
    Pages 1-18
  2. Introduction

    1. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 19-24
  3. Selfadjoint Operators in Hilbert Spaces

    1. Front Matter
      Pages 25-25
    2. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 26-40
    3. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 41-44
    4. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 45-66
    5. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 67-79
    6. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 80-93
  4. Algebras of Asymptotic Constants

    1. Front Matter
      Pages 95-96
    2. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 97-125
    3. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 126-148
    4. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 149-167
  5. Two-Space Wave Operators and Scattering Operators

    1. Front Matter
      Pages 169-169
    2. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 170-194
    3. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 195-232
    4. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 233-249
    5. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 250-263
    6. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 264-291
  6. Existence and Completeness of Wave Operators

    1. Front Matter
      Pages 299-300
    2. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 301-321
    3. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 322-342
    4. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 343-355
    5. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 356-374
  7. Some Properties of the Scattering Operator, the Scattering Matrix, and the Scattering Amplitude

    1. Front Matter
      Pages 381-381
    2. Hellmut Baumgärtel, Manfred Wollenberg
      Pages 400-417
  8. Back Matter
    Pages 420-449

About this book

Introduction

The aim of this book is to give a systematic and self-contained presentation of the Mathematical Scattering Theory within the framework of operator theory in Hilbert space. The term Mathematical Scattering Theory denotes that theory which is on the one hand the common mathematical foundation of several physical scattering theories (scattering of quantum objects, of classical waves and particles) and on the other hand a branch of operator theory devoted to the study of the behavior of the continuous part of perturbed operators (some authors also use the term Abstract Scattering Theory). EBBential contributions to the development of this theory are due to K. FRIEDRICHS, J. CooK, T. KATo, J. M. JAuCH, S. T. KURODA, M.S. BmMAN, M.G. KREiN, L. D. FAD­ DEEV, R. LAVINE, W. 0. AMREIN, B. SIMoN, D. PEARSON, V. ENss, and others. It seems to the authors that the theory has now reached a sufficiently developed state that a self-contained presentation of the topic is justified.

Keywords

behavior development framework Hilbert space Mathematica object operator operator theory presentation scattering theory Simon

Authors and affiliations

  • Hellmut Baumgärtel
    • 1
  • Manfred Wollenberg
    • 1
  1. 1.Institut für MathematikAkademie der Wissenschaften der DDRDeutschland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-5440-5
  • Copyright Information Birkhäuser Basel 1983
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-5442-9
  • Online ISBN 978-3-0348-5440-5
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site