Lecture Notes in Mathematics

Perturbation Theory for the Schrödinger Operator with a Periodic Potential

Authors: Karpeshina, Yulia E.

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About this book

The book is devoted to perturbation theory for the Schrödinger operator with a periodic potential, describing motion of a particle in bulk matter. The Bloch eigenvalues of the operator are densely situated in a high energy region, so regular perturbation theory is ineffective. The mathematical difficulties have a physical nature - a complicated picture of diffraction inside the crystal. The author develops a new mathematical approach to this problem. It provides mathematical physicists with important results for this operator and a new technique that can be effective for other problems. The semiperiodic Schrödinger operator, describing a crystal with a surface, is studied. Solid-body theory specialists can find asymptotic formulae, which are necessary for calculating many physical values.

Table of contents (5 chapters)

  • Introduction

    Karpeshina, Yulia E.

    Pages 1-22

  • Perturbation theory for a polyharmonic operator in the case of 2l>n

    Karpeshina, Yulia E.

    Pages 23-62

  • Perturbation theory for the polyharmonic operator in the case 4l>n+1

    Karpeshina, Yulia E.

    Pages 63-97

  • Perturbation theory for Schrödinger operator with a periodic potential

    Karpeshina, Yulia E.

    Pages 99-232

  • The interaction of a free wave with a semi-bounded crystal

    Karpeshina, Yulia E.

    Pages 233-338

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-540-69156-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-3-540-63136-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Perturbation Theory for the Schrödinger Operator with a Periodic Potential
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1663
Copyright
1997
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-69156-3
DOI
10.1007/BFb0094264
Softcover ISBN
978-3-540-63136-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
CCCLXIV, 356
Topics