Theoretical and Mathematical Physics

Inverse Problems in Quantum Scattering Theory

Authors: Chadan, Khosrow, Sabatier, Pierre C.

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About this book

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.

Table of contents (19 chapters)

  • Some Results from Scattering Theory

    Chadan, K. (et al.)

    Pages 1-19

  • Bound States—Eigenfunction Expansions

    Chadan, K. (et al.)

    Pages 20-39

  • The Gel’fand-Levitan-Jost-Kohn Method

    Chadan, K. (et al.)

    Pages 40-58

  • Applications of the Gel’fand-Levitan Equation

    Chadan, K. (et al.)

    Pages 59-75

  • The Marchenko Method

    Chadan, K. (et al.)

    Pages 76-85

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-642-83317-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for USA in USD
  • ISBN 978-3-642-83319-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Inverse Problems in Quantum Scattering Theory
Authors
Series Title
Theoretical and Mathematical Physics
Copyright
1989
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-3-642-83317-5
DOI
10.1007/978-3-642-83317-5
Softcover ISBN
978-3-642-83319-9
Series ISSN
1864-5879
Edition Number
2
Number of Pages
XXXI, 499
Topics