Spectral asymptotics in the semi-classical limit
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 p...
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| Sprache: | English |
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Cambridge
Cambridge University Press
1999
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| Schriftenreihe: | London Mathematical Society lecture note series
268 |
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| 520 | |a 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. | ||
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| spelling | Dimassi, Mouez Spectral asymptotics in the semi-classical limit Mouez Dimassi, Johannes Sjöstrand Cambridge Cambridge University Press 1999 1 Online-Ressource (xi, 227 Seiten) txt c cr London Mathematical Society lecture note series 268 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. Sjöstrand, J. Erscheint auch als Druck-Ausgabe 9780521665445 TUM01 ZDB-20-CTM TUM_PDA_CTM https://doi.org/10.1017/CBO9780511662195 Volltext |
| spellingShingle | Dimassi, Mouez Spectral asymptotics in the semi-classical limit |
| title | Spectral asymptotics in the semi-classical limit |
| title_auth | Spectral asymptotics in the semi-classical limit |
| title_exact_search | Spectral asymptotics in the semi-classical limit |
| title_full | Spectral asymptotics in the semi-classical limit Mouez Dimassi, Johannes Sjöstrand |
| title_fullStr | Spectral asymptotics in the semi-classical limit Mouez Dimassi, Johannes Sjöstrand |
| title_full_unstemmed | Spectral asymptotics in the semi-classical limit Mouez Dimassi, Johannes Sjöstrand |
| title_short | Spectral asymptotics in the semi-classical limit |
| title_sort | spectral asymptotics in the semi classical limit |
| url | https://doi.org/10.1017/CBO9780511662195 |
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