ENGLISH

Spectral Asymptotics in the Semi-Classical Limit

By J. Sjöstrand , M. Dimassi

Book information

Publisher
Cambridge University Press
Year
1999
ISBN
9780521665445, 0521665442, 9780511662195
LCC
QC20.7.M53 D56 1999
Language
english
Format
PDF
Filesize
2 MB (1999418 bytes)
Series
London Mathematical Society Lecture Note Series
Pages
240\240
Scanned
yes
Time added
2010-05-31 15:29:46

Description

Semiclassical approximation addresses the important relationship between quantum and classical mechanics. In recent years mathematical theory has undergone significant growth, mainly due to microlocal analysis techniques. This volume develops the basic methods of the theory, including the WKB-method, stationary phase and h-pseudodifferential operators. The authors employ the systematic use of a Cauchy formula that simplifies the functional calculus of pseudodifferential operators. The applications described include recent results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. The text assumes no previous specialized knowledge in quantum mechanics or microlocal analysis, and only general knowledge of spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry.

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