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

Format:

Book

Author/Creator:

Helffer, Bernard, author.

Series:

Nankai Institute of Mathematics, Tianjin, P.R. China ; 1336

Language:

English

Subjects (All):

Mathematical physics.

Quantum theory.

Mathematical analysis.

Theoretical, Mathematical and Computational Physics.

Quantum Physics.

Analysis.

Local Subjects:

Theoretical, Mathematical and Computational Physics.

Quantum Physics.

Analysis.

Physical Description:

1 online resource (V, 110 p.)

Edition:

1st ed. 1988.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1988.

Language Note:

English

Summary:

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.

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

ISBN:

3-540-45913-8

OCLC:

1066193714