Spectral asymptotics in the semi-classical limit /

Spectral asymptotics in the semi-classical limit /

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Bibliographic Details
Author / Creator:	Dimassi, Mouez.
Imprint:	Cambridge, U.K. ; New York : Cambridge University Press, 1999.
Description:	1 online resource (xi, 227 pages)
Language:	English
Series:	London Mathematical Society lecture note series ; 268 London Mathematical Society lecture note series ; 268.
Subject:	Microlocal analysis. Quantum theory. Approximation theory. Spectral theory (Mathematics) Mathematical physics. Approximation theory. Mathematical physics. Microlocal analysis. Quantum theory. Spectral theory (Mathematics) Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11181236

Hidden Bibliographic Details
Other authors / contributors:	Sjöstrand, J. (Johannes)
ISBN:	9781107362796 1107362792 9780511662195 051166219X 0521665442 9780521665445
Notes:	Includes bibliographical references (pages 209-220) and index. Print version record.
Summary:	Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include 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. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.
Other form:	Print version: Dimassi, Mouez. Spectral asymptotics in the semi-classical limit. Cambridge, U.K. ; New York : Cambridge University Press, 1999 0521665442

Table of Contents:

Local symplectic geometry
The WKB-method
The WKB-method for a potential minimum
Self-adjoint operators
The method of stationary phase
Tunnel effect and interaction matrix
@h-pseudodifferential operators
Functional calculus for pseudodifferential operators
Trace class operators and applications of the functional calculus
More precise spectral asymptotics for non-critical Hamiltonians
Improvement when the periodic trajectories form a set of measure 0
A more general study of the trace
Spectral theory for perturbed periodic problems
Normal forms for some scalar pseudodifferential operators
Spectrum of operators with periodic bicharacteristics.