C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1996
|
| Schriftenreihe: | Progress in Mathematics
135 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The relevance of commutator methods in spectral and scattering theory has been known for a long time, and numerous interesting results have been ob tained by such methods. The reader may find a description and references in the books by Putnam [Pu], Reed-Simon [RS] and Baumgartel-Wollenberg [BW] for example. A new point of view emerged around 1979 with the work of E. Mourre in which the method of locally conjugate operators was introduced. His idea proved to be remarkably fruitful in establishing detailed spectral properties of N-body Hamiltonians. A problem that was considered extremely difficult be fore that time, the proof of the absence of a singularly continuous spectrum for such operators, was then solved in a rather straightforward manner (by E. Mourre himself for N = 3 and by P. Perry, 1. Sigal and B. Simon for general N). The Mourre estimate, which is the main input of the method, also has consequences concerning the behaviour of N-body systems at large times. A deeper study of such propagation properties allowed 1. Sigal and A. Soffer in 1985 to prove existence and completeness of wave operators for N-body systems with short range interactions without implicit conditions on the potentials (for N = 3, similar results were obtained before by means of purely time-dependent methods by V. Enss and by K. Sinha, M. Krishna and P. Muthuramalingam). Our interest in commutator methods was raised by the major achievements mentioned above |
| Beschreibung: | 1 Online-Ressource (XIV, 464 p) |
| ISBN: | 9783034877626 9783034877640 |
| DOI: | 10.1007/978-3-0348-7762-6 |
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Datensatz im Suchindex
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| author | Amrein, Werner O. |
| author_facet | Amrein, Werner O. |
| author_role | aut |
| author_sort | Amrein, Werner O. |
| author_variant | w o a wo woa |
| building | Verbundindex |
| bvnumber | BV042421962 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879624733 (DE-599)BVBBV042421962 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-7762-6 |
| format | Electronic eBook |
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| id | DE-604.BV042421962 |
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| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034877626 9783034877640 |
| language | English |
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| publishDate | 1996 |
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| spelling | Amrein, Werner O. Verfasser aut C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians by Werner O. Amrein, Anne Boutet Monvel, Vladimir Georgescu Basel Birkhäuser Basel 1996 1 Online-Ressource (XIV, 464 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 135 The relevance of commutator methods in spectral and scattering theory has been known for a long time, and numerous interesting results have been ob tained by such methods. The reader may find a description and references in the books by Putnam [Pu], Reed-Simon [RS] and Baumgartel-Wollenberg [BW] for example. A new point of view emerged around 1979 with the work of E. Mourre in which the method of locally conjugate operators was introduced. His idea proved to be remarkably fruitful in establishing detailed spectral properties of N-body Hamiltonians. A problem that was considered extremely difficult be fore that time, the proof of the absence of a singularly continuous spectrum for such operators, was then solved in a rather straightforward manner (by E. Mourre himself for N = 3 and by P. Perry, 1. Sigal and B. Simon for general N). The Mourre estimate, which is the main input of the method, also has consequences concerning the behaviour of N-body systems at large times. A deeper study of such propagation properties allowed 1. Sigal and A. Soffer in 1985 to prove existence and completeness of wave operators for N-body systems with short range interactions without implicit conditions on the potentials (for N = 3, similar results were obtained before by means of purely time-dependent methods by V. Enss and by K. Sinha, M. Krishna and P. Muthuramalingam). Our interest in commutator methods was raised by the major achievements mentioned above Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik Selbstadjungierter Operator (DE-588)4180810-1 gnd rswk-swf Dreikörperproblem (DE-588)4012974-3 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Kommutator Quantentheorie (DE-588)4164827-4 gnd rswk-swf Dreikörperproblem (DE-588)4012974-3 s Hamilton-Operator (DE-588)4072278-8 s Selbstadjungierter Operator (DE-588)4180810-1 s Spektraltheorie (DE-588)4116561-5 s Kommutator Quantentheorie (DE-588)4164827-4 s 1\p DE-604 Monvel, Anne Boutet Sonstige oth Georgescu, Vladimir Sonstige oth https://doi.org/10.1007/978-3-0348-7762-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Amrein, Werner O. C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik Selbstadjungierter Operator (DE-588)4180810-1 gnd Dreikörperproblem (DE-588)4012974-3 gnd Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd Kommutator Quantentheorie (DE-588)4164827-4 gnd |
| subject_GND | (DE-588)4180810-1 (DE-588)4012974-3 (DE-588)4072278-8 (DE-588)4116561-5 (DE-588)4164827-4 |
| title | C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians |
| title_auth | C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians |
| title_exact_search | C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians |
| title_full | C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians by Werner O. Amrein, Anne Boutet Monvel, Vladimir Georgescu |
| title_fullStr | C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians by Werner O. Amrein, Anne Boutet Monvel, Vladimir Georgescu |
| title_full_unstemmed | C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians by Werner O. Amrein, Anne Boutet Monvel, Vladimir Georgescu |
| title_short | C 0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians |
| title_sort | c 0 groups commutator methods and spectral theory of n body hamiltonians |
| topic | Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik Selbstadjungierter Operator (DE-588)4180810-1 gnd Dreikörperproblem (DE-588)4012974-3 gnd Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd Kommutator Quantentheorie (DE-588)4164827-4 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Theoretical, Mathematical and Computational Physics Mathematik Selbstadjungierter Operator Dreikörperproblem Hamilton-Operator Spektraltheorie Kommutator Quantentheorie |
| url | https://doi.org/10.1007/978-3-0348-7762-6 |
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