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Overview
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.
Synopsis
This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Booknews
A textbook developed from a one-semester course for graduates and researchers in mathematical analysis and physics. Dimassi (U. de Paris-Nord) and Sj<:o>strang (Ecole Polytechnique) include more recent material than classical studies of spectral asymptotics, but attempt to keep the treatment at an introductory level. Among their applications are results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, and the slow perturbation of periodic Schr<:o>dinger operators in solid-state physics. Annotation c. Book News, Inc., Portland, OR (booknews.com)