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Inverse Problems in Quantum Scattering Theory

  • K. Chadan
  • P. C. Sabatier
  • R. G. Newton

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xxxi
  2. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 1-19
  3. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 20-39
  4. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 40-58
  5. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 59-75
  6. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 76-85
  7. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 86-94
  8. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 95-111
  9. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 112-127
  10. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 128-154
  11. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 155-181
  12. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 195-213
  13. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 214-234
  14. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 235-274
  15. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 275-289
  16. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 290-322
  17. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 323-388
  18. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 389-415
  19. K. Chadan, P. C. Sabatier, R. G. Newton
    Pages 416-439
  20. Back Matter
    Pages 441-499

About this book

Introduction

The normal business of physicists may be schematically thought of as predic­ ting the motions of particles on the basis of known forces, or the propagation of radiation on the basis of a known constitution of matter. The inverse problem is to conclude what the forces or constitutions are on the basis of the observed motion. A large part of our sensory contact with the world around us depends on an intuitive solution of such an inverse problem: We infer the shape, size, and surface texture of external objects from their scattering and absorption of light as detected by our eyes. When we use scattering experiments to learn the size or shape of particles, or the forces they exert upon each other, the nature of the problem is similar, if more refined. The kinematics, the equations of motion, are usually assumed to be known. It is the forces that are sought, and how they vary from point to point. As with so many other physical ideas, the first one we know of to have touched upon the kind of inverse problem discussed in this book was Lord Rayleigh (1877). In the course of describing the vibrations of strings of variable density he briefly discusses the possibility of inferring the density distribution from the frequencies of vibration. This passage may be regarded as a precursor of the mathematical study of the inverse spectral problem some seventy years later.

Keywords

Inverses Streuproblem Potential calculus inverse scattering problem inverse scattering theory numerical methods scattering theory

Authors and affiliations

  • K. Chadan
    • 1
  • P. C. Sabatier
    • 2
  • R. G. Newton
    • 3
  1. 1.Laboratoire de Physique ThéoriqueUniversité de Paris-SudOrsayFrance
  2. 2.Université des Sciences et Techniques du LanguedocMontpellier CedexFrance
  3. 3.Department of PhysicsIndiana UniversityBloomingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-83317-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-83319-9
  • Online ISBN 978-3-642-83317-5
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site