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Semi-Classical Analysis for the Schrödinger Operator and Applications

  • Book
  • © 1988

Overview

Authors:
  1. Bernard Helffer
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1336)

Part of the book sub series: Nankai Institute of Mathematics, Tianjin, P.R. China (2803)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-V
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  2. Generalities on semi-classical analysis

    • Bernard Helffer
    Pages 1-6

  3. B.K.W. Construction for a potential near the bottom in the case of non-degenerate minima

    • Bernard Helffer
    Pages 7-18

  4. The decay of the eigenfunctions

    • Bernard Helffer
    Pages 19-29

  5. Study of interaction between the wells

    • Bernard Helffer
    Pages 30-60

  6. An introduction to recent results of Witten

    • Bernard Helffer
    Pages 61-70

  7. On Schrödinger operators with periodic electric potentials

    • Bernard Helffer
    Pages 71-78

  8. On Schrödinger operators with magnetic fields

    • Bernard Helffer
    Pages 79-99

  9. Back Matter

    Pages 100-107
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Semi-Classical Analysis for the Schrödinger Operator and Applications

  • Authors: Bernard Helffer

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0078115

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-50076-6Published: 27 July 1988

  • eBook ISBN: 978-3-540-45913-2Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: V, 110

  • Topics: Theoretical, Mathematical and Computational Physics, Quantum Physics, Analysis

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