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:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, U.K. ; New York :
Cambridge University Press,
1999.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
268. |
| Schlagworte: | |
| Online-Zugang: | 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: | 1 online resource (xi, 227 pages) |
| Bibliographie: | Includes bibliographical references (pages 209-220) and index. |
| ISBN: | 9781107362796 1107362792 9780511662195 051166219X |
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| 505 | 0 | 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. |
| 588 | 0 | |a Print version record. | |
| 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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| 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. |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
| isbn | 9781107362796 1107362792 9780511662195 051166219X |
| language | English |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Dimassi, Mouez. Spectral asymptotics in the semi-classical limit / Mouez Dimassi, Johannes Sjöstrand. Cambridge, U.K. ; New York : Cambridge University Press, 1999. 1 online resource (xi, 227 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 268 Includes bibliographical references (pages 209-220) and index. 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. Print version record. 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. Microlocal analysis. http://id.loc.gov/authorities/subjects/sh92003594 Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Spectral theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85126408 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Analyse microlocale. Théorie quantique. Théorie de l'approximation. Spectre (Mathématiques) Physique mathématique. SCIENCE Physics Mathematical & Computational. bisacsh Approximation theory fast Mathematical physics fast Microlocal analysis fast Quantum theory fast Spectral theory (Mathematics) fast Quasiklassische Näherung gnd http://d-nb.info/gnd/4296820-3 Analyse (wiskunde) gtt Operadores microlocais. larpcal Approximation, Théorie de l'. ram Théorie quantique. ram Physique mathématique Théorie asymptotique. ram Théorie spectrale (Mathématiques) ram Valeurs propres. ram Mécanique. ram Sjöstrand, J. (Johannes) https://id.oclc.org/worldcat/entity/E39PBJwD4M6hYCb9Dbh8jjdbBP http://id.loc.gov/authorities/names/n88630485 Print version: Dimassi, Mouez. Spectral asymptotics in the semi-classical limit. Cambridge, U.K. ; New York : Cambridge University Press, 1999 0521665442 (DLC) 00267617 (OCoLC)41338809 London Mathematical Society lecture note series ; 268. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552456 Volltext |
| spellingShingle | Dimassi, Mouez Spectral asymptotics in the semi-classical limit / London Mathematical Society lecture note series ; 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. Microlocal analysis. http://id.loc.gov/authorities/subjects/sh92003594 Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Spectral theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85126408 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Analyse microlocale. Théorie quantique. Théorie de l'approximation. Spectre (Mathématiques) Physique mathématique. SCIENCE Physics Mathematical & Computational. bisacsh Approximation theory fast Mathematical physics fast Microlocal analysis fast Quantum theory fast Spectral theory (Mathematics) fast Quasiklassische Näherung gnd http://d-nb.info/gnd/4296820-3 Analyse (wiskunde) gtt Operadores microlocais. larpcal Approximation, Théorie de l'. ram Théorie quantique. ram Physique mathématique Théorie asymptotique. ram Théorie spectrale (Mathématiques) ram Valeurs propres. ram Mécanique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh92003594 http://id.loc.gov/authorities/subjects/sh85109469 http://id.loc.gov/authorities/subjects/sh85006190 http://id.loc.gov/authorities/subjects/sh85126408 http://id.loc.gov/authorities/subjects/sh85082129 https://id.nlm.nih.gov/mesh/D011789 http://d-nb.info/gnd/4296820-3 |
| 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 | Microlocal analysis. http://id.loc.gov/authorities/subjects/sh92003594 Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Approximation theory. http://id.loc.gov/authorities/subjects/sh85006190 Spectral theory (Mathematics) http://id.loc.gov/authorities/subjects/sh85126408 Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Analyse microlocale. Théorie quantique. Théorie de l'approximation. Spectre (Mathématiques) Physique mathématique. SCIENCE Physics Mathematical & Computational. bisacsh Approximation theory fast Mathematical physics fast Microlocal analysis fast Quantum theory fast Spectral theory (Mathematics) fast Quasiklassische Näherung gnd http://d-nb.info/gnd/4296820-3 Analyse (wiskunde) gtt Operadores microlocais. larpcal Approximation, Théorie de l'. ram Théorie quantique. ram Physique mathématique Théorie asymptotique. ram Théorie spectrale (Mathématiques) ram Valeurs propres. ram Mécanique. ram |
| topic_facet | Microlocal analysis. Quantum theory. Approximation theory. Spectral theory (Mathematics) Mathematical physics. Quantum Theory Analyse microlocale. Théorie quantique. Théorie de l'approximation. Spectre (Mathématiques) Physique mathématique. SCIENCE Physics Mathematical & Computational. Approximation theory Mathematical physics Microlocal analysis Quantum theory Quasiklassische Näherung Analyse (wiskunde) Operadores microlocais. Approximation, Théorie de l'. Physique mathématique Théorie asymptotique. Théorie spectrale (Mathématiques) Valeurs propres. Mécanique. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552456 |
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