Semi-classical analysis for the Schrödinger operator and applications /

Semi-classical analysis for the Schrödinger operator and applications /

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Bibliographic Details
Author / Creator:	Helffer, Bernard.
Imprint:	Berlin ; New York : Springer-Verlag, ©1988.
Description:	1 online resource (iv, 107 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1336 Lecture notes in mathematics (Springer-Verlag) ; 1336.
Subject:	Schrödinger operator. Differential equations, Partial -- Asymptotic theory. Spectral theory (Mathematics) Differential equations, Partial -- Asymptotic theory. Schrödinger operator. Spectral theory (Mathematics)
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11071299

Hidden Bibliographic Details
ISBN:	9783540459132 3540459138 9780387500768 0387500766 9783540500766 3540500766
Notes:	Includes bibliographical references (pages 100-105) and index. Restrictions unspecified Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 digitized 2010 HathiTrust Digital Library committed to preserve Print version record.
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 Schrdinger operator with periodic potentials.
Other form:	Print version: Helffer, Bernard. Semi-classical analysis for the Schrödinger operator and applications. Berlin ; New York : Springer-Verlag, ©1988 3540500766

Table of Contents:

Generalities on Semi-Classical Analysis
B.K.W. Construction for a Potential Near the Bottom in the Case of Nondegenerate Minima
The Decay of the Eigenfunctions
Study of Interaction Between the Wells
An Introduction to Recent Results of Witten
On Schrdinger Operators with Periodic Electric Potentials
On Schrdinger Operators with Magnetic Fields
References
Index.