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...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
|
| Schriftenreihe: | London Mathematical Society lecture note series
268 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xi, 227 pages) |
| ISBN: | 9780511662195 |
| DOI: | 10.1017/CBO9780511662195 |
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| 505 | 8 | 0 | |t Local symplectic geometry |t The WKB-method |t The WKB-method for a potential minimum |t Self-adjoint operators |t The method of stationary phase |t Tunnel effect and interaction matrix |t @h-pseudodifferential operators |t Functional calculus for pseudodifferential operators |t Trace class operators and applications of the functional calculus |t More precise spectral asymptotics for non-critical Hamiltonians |t Improvement when the periodic trajectories form a set of measure 0 |t A more general study of the trace |t Spectral theory for perturbed periodic problems |t Normal forms for some scalar pseudodifferential operators |t Spectrum of operators with periodic bicharacteristics |
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Datensatz im Suchindex
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| author | Dimassi, Mouez |
| author_facet | Dimassi, Mouez |
| author_role | aut |
| author_sort | Dimassi, Mouez |
| author_variant | m d md |
| building | Verbundindex |
| bvnumber | BV043942348 |
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| contents | Local symplectic geometry The WKB-method The WKB-method for a potential minimum Self-adjoint operators The method of stationary phase Tunnel effect and interaction matrix @h-pseudodifferential operators Functional calculus for pseudodifferential operators Trace class operators and applications of the functional calculus More precise spectral asymptotics for non-critical Hamiltonians Improvement when the periodic trajectories form a set of measure 0 A more general study of the trace Spectral theory for perturbed periodic problems Normal forms for some scalar pseudodifferential operators Spectrum of operators with periodic bicharacteristics |
| ctrlnum | (ZDB-20-CBO)CR9780511662195 (OCoLC)967776398 (DE-599)BVBBV043942348 |
| dewey-full | 530.15/57222 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15/57222 |
| dewey-search | 530.15/57222 |
| dewey-sort | 3530.15 557222 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511662195 |
| format | Electronic eBook |
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| id | DE-604.BV043942348 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511662195 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351318 |
| oclc_num | 967776398 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xi, 227 pages) |
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| spelling | Dimassi, Mouez Verfasser aut Spectral asymptotics in the semi-classical limit Mouez Dimassi, Johannes Sjöstrand Cambridge Cambridge University Press 1999 1 online resource (xi, 227 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 268 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Local symplectic geometry The WKB-method The WKB-method for a potential minimum Self-adjoint operators The method of stationary phase Tunnel effect and interaction matrix @h-pseudodifferential operators Functional calculus for pseudodifferential operators Trace class operators and applications of the functional calculus More precise spectral asymptotics for non-critical Hamiltonians Improvement when the periodic trajectories form a set of measure 0 A more general study of the trace Spectral theory for perturbed periodic problems Normal forms for some scalar pseudodifferential operators Spectrum of operators with periodic bicharacteristics 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 Mathematische Physik Quantentheorie Microlocal analysis Quantum theory Approximation theory Spectral theory (Mathematics) Mathematical physics Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 gnd rswk-swf WKB-Methode (DE-588)4190133-2 gnd rswk-swf Quasiklassische Näherung (DE-588)4296820-3 gnd rswk-swf Mikrolokale Analysis (DE-588)4169832-0 gnd rswk-swf WKB-Methode (DE-588)4190133-2 s Spektraltheorie (DE-588)4116561-5 s Pseudodifferentialoperator (DE-588)4047640-6 s Mikrolokale Analysis (DE-588)4169832-0 s 1\p DE-604 Quasiklassische Näherung (DE-588)4296820-3 s 2\p DE-604 Sjöstrand, J. Sonstige oth Erscheint auch als Druckausgabe 978-0-521-66544-5 https://doi.org/10.1017/CBO9780511662195 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Dimassi, Mouez Spectral asymptotics in the semi-classical limit Local symplectic geometry The WKB-method The WKB-method for a potential minimum Self-adjoint operators The method of stationary phase Tunnel effect and interaction matrix @h-pseudodifferential operators Functional calculus for pseudodifferential operators Trace class operators and applications of the functional calculus More precise spectral asymptotics for non-critical Hamiltonians Improvement when the periodic trajectories form a set of measure 0 A more general study of the trace Spectral theory for perturbed periodic problems Normal forms for some scalar pseudodifferential operators Spectrum of operators with periodic bicharacteristics Mathematische Physik Quantentheorie Microlocal analysis Quantum theory Approximation theory Spectral theory (Mathematics) Mathematical physics Spektraltheorie (DE-588)4116561-5 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd WKB-Methode (DE-588)4190133-2 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4047640-6 (DE-588)4190133-2 (DE-588)4296820-3 (DE-588)4169832-0 |
| title | Spectral asymptotics in the semi-classical limit |
| title_alt | Local symplectic geometry The WKB-method The WKB-method for a potential minimum Self-adjoint operators The method of stationary phase Tunnel effect and interaction matrix @h-pseudodifferential operators Functional calculus for pseudodifferential operators Trace class operators and applications of the functional calculus More precise spectral asymptotics for non-critical Hamiltonians Improvement when the periodic trajectories form a set of measure 0 A more general study of the trace Spectral theory for perturbed periodic problems Normal forms for some scalar pseudodifferential operators Spectrum of operators with periodic bicharacteristics |
| 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 |
| topic | Mathematische Physik Quantentheorie Microlocal analysis Quantum theory Approximation theory Spectral theory (Mathematics) Mathematical physics Spektraltheorie (DE-588)4116561-5 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd WKB-Methode (DE-588)4190133-2 gnd Quasiklassische Näherung (DE-588)4296820-3 gnd Mikrolokale Analysis (DE-588)4169832-0 gnd |
| topic_facet | Mathematische Physik Quantentheorie Microlocal analysis Quantum theory Approximation theory Spectral theory (Mathematics) Mathematical physics Spektraltheorie Pseudodifferentialoperator WKB-Methode Quasiklassische Näherung Mikrolokale Analysis |
| url | https://doi.org/10.1017/CBO9780511662195 |
| work_keys_str_mv | AT dimassimouez spectralasymptoticsinthesemiclassicallimit AT sjostrandj spectralasymptoticsinthesemiclassicallimit |