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Spectral Asymptotics in the Semi-Classical Limit : London Mathematical Society Lecture Note Series - M. Dimassi

Spectral Asymptotics in the Semi-Classical Limit

By: M. Dimassi, Mouez Dimassi, J. Sjostrand

Paperback | 15 November 1999

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Semiclassical approximation addresses the important relationship between quantum and classical mechanics. In recent years 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 recent results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrodinger 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.
Industry Reviews
'... recommended to everyone, be it student or researcher, who is interested in semiclassical analysis.' Zentralblatt MATH 'This book is an excellent introduction to a modern rapidly developing subject which lies between mathematics and physics.' Yuri Safarov, Bulletin of the London Mathematical Society

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