Lecture Notes in Mathematics

Scattering Theory: Some Old and New Problems

Authors: Yafaev, Dmitri R.

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About this book

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.

Table of contents (17 chapters)

  • Basic concepts

    Yafaev, Dmitri R.

    Pages 1-13

  • Short-range interactions. asymptotic completeness

    Yafaev, Dmitri R.

    Pages 14-23

  • Short-range interactions. Miscellaneous

    Yafaev, Dmitri R.

    Pages 24-29

  • Long-range interactions. The scheme of smooth perturbations

    Yafaev, Dmitri R.

    Pages 30-39

  • The generalized fourier transform

    Yafaev, Dmitri R.

    Pages 40-46

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-540-45170-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-3-540-67587-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Scattering Theory: Some Old and New Problems
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1735
Copyright
2000
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-45170-9
DOI
10.1007/BFb0105531
Softcover ISBN
978-3-540-67587-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVI, 176
Topics