Semi-Classical Analysis for the Schrödinger Operator and Applications

Häftad, Engelska, 1988

Del 1336 i serien Lecture Notes in Mathematics

278 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:1988-07-27
Mått:155 x 235 x 7 mm
Vikt:195 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:110
Upplaga:1988
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540500766

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Innehållsförteckning

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.