Spectral Asymptotics in the Semi-Classical Limit (London Mathematical Society Lecture Note Series, Series Number 268) 1st Edition by M. Dimassi | (PDF) Free Download

Description

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.

User’s Reviews

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 This book presents the basic methods and applications in semiclassical approximation in the light of developments.

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⭐半古典極限に関する手ごろな入門書である。とくに、応用分野である量子力学のスペクトル論をにらんで、応用上重要となるスペクトルの漸近解析を学ぶ上で役に立つ入門書である。全体がコンパクトにまとめられているため、基礎事項を要領よく学ぶことができる。

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Free Download Spectral Asymptotics in the Semi-Classical Limit (London Mathematical Society Lecture Note Series, Series Number 268) 1st Edition in PDF format
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Spectral Asymptotics in the Semi-Classical Limit (London Mathematical Society Lecture Note Series, Series Number 268) 1st Edition 1999 PDF Free Download
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