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  3. Spectral Asymptotics in the Semi-Classical Limit
  • Cited by 396
Publisher:
Cambridge University Press
Online publication date:
March 2010
Print publication year:
1999
Online ISBN:
9780511662195
DOI:
https://doi.org/10.1017/CBO9780511662195
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
London Mathematical Society Lecture Note Series (268)
Information

Book description

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.

Reviews

‘… recommended to everyone, be it student or researcher, who is interested in semiclassical analysis.’

Source: Zentralblatt MATH

‘This book is an excellent introduction to a modern rapidly developing subject which lies between mathematics and physics.’

Yuri Safarov Source: Bulletin of the London Mathematical Society

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