Spectral Asymptotics in the Semi-Classical Limit (London Mathematical Society Lecture Note Series) [Paperback]

M. Dimassi (Author), J. Sjostrand (Author)

Book Description

Publication Date: October 13, 1999 | ISBN-10: 0521665442 | ISBN-13: 978-0521665445

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.

Editorial Reviews

Review

"Researchers and graduate students in mathematical analysis are the intended readership, but anyone with an interest in the current state of the mathematics of quantum mechanics will get a lot out of this book." Proceedings of the Edinburgh Mathematical Society

"The authors have managed to write a very useful, clear, and readable book of quite moderate size, applying modern sophisticated methods in order to attack successfully some important, interesting, and difficult problems of contemporary mathematical physics." Mathematical Reviews

Book Description

Semiclassical approximation addresses the important relationship between quantum and classical mechanics. This book presents the basic methods in the light of recent developments, including the WKB-method, stationary phase and h-pseudodifferential operators. Applications include the tunnel effect, asymptotics of eigenvalues, plus slow perturbations of periodic Schrödinger operators in solid state physics. 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.

Product Details

• Paperback: 240 pages
• Publisher: Cambridge University Press (October 13, 1999)
• Language: English
• ISBN-10: 0521665442
• ISBN-13: 978-0521665445
• Product Dimensions: 8.8 x 6 x 0.6 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Amazon Best Sellers Rank: #2,847,153 in Books (See Top 100 in Books)

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