Semi-Classical Analysis for the Schrödinger Operator and Applications

  • Authors
  • Bernard Helffer

Part of the Lecture Notes in Mathematics book series (LNM, volume 1336)

Table of contents

  1. Front Matter
    Pages I-V
  2. Bernard Helffer
    Pages 1-6
  3. Bernard Helffer
    Pages 19-29
  4. Bernard Helffer
    Pages 30-60
  5. Bernard Helffer
    Pages 61-70
  6. Back Matter
    Pages 100-107

About this book

Introduction

This introduction to semi-classical analysis is an extension of a course given by the author at the University of Nankai. It presents for some of the standard cases presented in quantum mechanics books a rigorous study of the tunneling effect, as an introduction to recent research work. The book may be read by a graduate student familiar with the classic book of Reed-Simon, and for some chapters basic notions in differential geometry. The mathematician will find here a nice application of PDE techniques and the physicist will discover the precise link between approximate solutions (B.K.W. constructions) and exact eigenfunctions (in every dimension). An application to Witten's approach for the proof of the Morse inequalities is given, as are recent results for the Schrödinger operator with periodic potentials.

Keywords

Potential calculus differential equation minimum quantum mechanics

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0078115
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-50076-6
  • Online ISBN 978-3-540-45913-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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