Semi-classical analysis for the Schrödinger operator and applications
Author(s)
Bibliographic Information
Semi-classical analysis for the Schrödinger operator and applications
（Lecture notes in mathematics, 1336 . Nankai Institute of Mathematics ; v. 4）
Springer-Verlag, c1988
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- : us
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Library & Science Information Center, Osaka Prefecture University
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
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Note
Bibliography: p. [100]-105
Includes index
Description and Table of Contents
Description
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 Schroedinger operator with periodic potentials.
Table of Contents
Generalities on semi-classical analysis.- B.K.W. Construction for a potential near the bottom in the case of non-degenerate minima.- The decay of the eigenfunctions.- Study of interaction between the wells.- An introduction to recent results of Witten.- On Schroedinger operators with periodic electric potentials.- On Schroedinger operators with magnetic fields.
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