Semi-Classical Analysis for the Schrödinger Operator and Applications by Bernard Helffer

Semi-Classical Analysis for the Schrödinger Operator and Applications

byBernard Helffer

Paperback | July 27, 1988

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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.
Title:Semi-Classical Analysis for the Schrödinger Operator and ApplicationsFormat:PaperbackProduct dimensions:112 pages, 9.25 X 6.1 X 0 inShipping dimensions:112 pages, 9.25 X 6.1 X 0 inPublished:July 27, 1988Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540500766

ISBN - 13:9783540500766

Appropriate for ages: All ages

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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 Schrödinger operators with periodic electric potentials.- On Schrödinger operators with magnetic fields.