Perturbation Theory for the Schrödinger Operator with a Periodic Potential

  • Authors
  • Yulia E. Karpeshina
Part of the Lecture Notes in Mathematics book series (LNM, volume 1663)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Yulia E. Karpeshina
    Pages 1-22
  3. Back Matter
    Pages 339-352

About this book

Introduction

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.

Keywords

Potential Schrödinger equation operator periodicity perturbation theory

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0094264
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63136-1
  • Online ISBN 978-3-540-69156-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692