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  • © 1997

Perturbation Theory for the Schrödinger Operator with a Periodic Potential

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1663)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VII
  2. Introduction

    • Yulia E. Karpeshina
    Pages 1-22
  3. Back Matter

    Pages 339-352

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.

Keywords

  • Potential
  • Schrödinger equation
  • operator
  • periodicity
  • perturbation theory
  • partial differential equations

Bibliographic Information

  • Book Title: Perturbation Theory for the Schrödinger Operator with a Periodic Potential

  • Authors: Yulia E. Karpeshina

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0094264

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-63136-1Published: 19 August 1997

  • eBook ISBN: 978-3-540-69156-3Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: CCCLXIV, 356

  • Topics: Differential Equations, Theoretical, Mathematical and Computational Physics

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions