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Nankai Institute of Mathematics, Tianjin, P.R. China

Semi-Classical Analysis for the Schrödinger Operator and Applications

Authors: Helffer, Bernard

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  • ISBN 978-3-540-45913-2
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  • ISBN 978-3-540-50076-6
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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.

Table of contents (7 chapters)

  • Generalities on semi-classical analysis

    Helffer, Bernard

    Pages 1-6

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

    Helffer, Bernard

    Pages 7-18

  • The decay of the eigenfunctions

    Helffer, Bernard

    Pages 19-29

  • Study of interaction between the wells

    Helffer, Bernard

    Pages 30-60

  • An introduction to recent results of Witten

    Helffer, Bernard

    Pages 61-70

Buy this book

eBook $29.99
price for USA (gross)
  • ISBN 978-3-540-45913-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA
  • ISBN 978-3-540-50076-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Semi-Classical Analysis for the Schrödinger Operator and Applications
Authors
Series Title
Nankai Institute of Mathematics, Tianjin, P.R. China
Series Volume
1336
Copyright
1988
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-45913-2
DOI
10.1007/BFb0078115
Softcover ISBN
978-3-540-50076-6
Edition Number
1
Number of Pages
V, 110
Topics