Methods of modern mathematical physics: 3 Scattering theory
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
2003
|
| Ausgabe: | [Nachdr.] |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 463 S. graph. Darst. |
| ISBN: | 012395827x 0125850034 9780125850032 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804135038095196160 |
|---|---|
| adam_text | Titel: Bd. 3. Methods of modern mathematical physics. Scattering theory
Autor: Reed, Michael
Jahr: 2003
Contents
Preface vii
Introduction ix
Contents of Other Volumes xv
XI: SCATTERING THEORY
/. An overview of scattering phenomena 1
2. Classical particle scattering 5
3. The basic principles of scattering in Hilbert space 16
Appendix 1 Stationary phase methods 37
Appendix 2 Trace ideal properties off(x)g{-N) 47
Appendix 3 A general invariance principle for wave operators 49
4. Quantum scattering I: Two-body case 54
5. Quantum scattering II: N-body case 75
6. Quantum scattering III: Eigenfunction expansions 96
Appendix Introduction to eigenfunction expansions by the
auxiliary space method 112
7. Quantum scattering IV: Dispersion relations 116
8. Quantum scattering V: Central potentials 121
A. Reduction of the S-matrix by symmetries 121
B. The partial wave expansion and its convergence 127
C. Phase shifts and their connection to the Schrodinger
equation 129
D. The variable phase equation 133
E. Jost functions and Levinson s theorem 136
F. Analyticity of the partial wave amplitude for generalized
Yukawa potentials 143
G. The Kohn variational principle 147
Appendix 1 Legendre polynomials and spherical Bessel
functions 149
Appendix 2 Jost solutions for oscillatory potentials 155
Appendix 3 Jost solutions and the fundamental problems of
scattering theory 164
9. Long-range potentials 169
10. Optical and acoustical scattering I: Schrodinger operator
methods 184
Appendix Trace class properties of Greens functions 203
11. Optical and acoustical scattering II: The Lax-Phillips
method 210
Appendix The twisting trick 241
12. The linear Boltzmann equation 243
13. Nonlinear wave equations 252
Appendix Conserved currents 278
14. Spin wave scattering 285
15. Quantum field scattering I: The external field 293
16. Quantum field scattering II: The Haag-Ruelle theory 317
17. Phase space analysis of scattering and spectral theory 331
Appendix The RAGE theorem 340
Notes 344
Notes on scattering theory on C*-algebras 382
Problems 385
MATERIAL PREPRINTED FROM VOLUME IV
XII 1.6 The absence of singular continuous spectrum I: General
theory 406
XI 11.7 The absence of singular continuous spectrum II: Smooth
perturbations 411
A. Weakly coupled quantum systems 421
B. Positive commutators and repulsive potentials 427
C. Local smoothness and wave operators for repulsive
potentials 433
XII 1.8 The absence of singular continuous spectrum III:
Weighted L1 spaces 438
Notes 447
Problems 450
List of Symbols 455
Index 457
|
| adam_txt |
Titel: Bd. 3. Methods of modern mathematical physics. Scattering theory
Autor: Reed, Michael
Jahr: 2003
Contents
Preface vii
Introduction ix
Contents of Other Volumes xv
XI: SCATTERING THEORY
/. An overview of scattering phenomena 1
2. Classical particle scattering 5
3. The basic principles of scattering in Hilbert space 16
Appendix 1 Stationary phase methods 37
Appendix 2 Trace ideal properties off(x)g{-N) 47
Appendix 3 A general invariance principle for wave operators 49
4. Quantum scattering I: Two-body case 54
5. Quantum scattering II: N-body case 75
6. Quantum scattering III: Eigenfunction expansions 96
Appendix Introduction to eigenfunction expansions by the
auxiliary space method 112
7. Quantum scattering IV: Dispersion relations 116
8. Quantum scattering V: Central potentials 121
A. Reduction of the S-matrix by symmetries 121
B. The partial wave expansion and its convergence 127
C. Phase shifts and their connection to the Schrodinger
equation 129
D. The variable phase equation 133
E. Jost functions and Levinson's theorem 136
F. Analyticity of the partial wave amplitude for generalized
Yukawa potentials 143
G. The Kohn variational principle 147
Appendix 1 Legendre polynomials and spherical Bessel
functions 149
Appendix 2 Jost solutions for oscillatory potentials 155
Appendix 3 Jost solutions and the fundamental problems of
scattering theory 164
9. Long-range potentials 169
10. Optical and acoustical scattering I: Schrodinger operator
methods 184
Appendix Trace class properties of Greens functions 203
11. Optical and acoustical scattering II: The Lax-Phillips
method 210
Appendix The twisting trick 241
12. The linear Boltzmann equation 243
13. Nonlinear wave equations 252
Appendix Conserved currents 278
14. Spin wave scattering 285
15. Quantum field scattering I: The external field 293
16. Quantum field scattering II: The Haag-Ruelle theory 317
17. Phase space analysis of scattering and spectral theory 331
Appendix The RAGE theorem 340
Notes 344
Notes on scattering theory on C*-algebras 382
Problems 385
MATERIAL PREPRINTED FROM VOLUME IV
XII 1.6 The absence of singular continuous spectrum I: General
theory 406
XI 11.7 The absence of singular continuous spectrum II: Smooth
perturbations 411
A. Weakly coupled quantum systems 421
B. Positive commutators and repulsive potentials 427
C. Local smoothness and wave operators for repulsive
potentials 433
XII 1.8 The absence of singular continuous spectrum III:
Weighted L1 spaces 438
Notes 447
Problems 450
List of Symbols 455
Index 457 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T13:42:27Z |
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| isbn | 012395827x 0125850034 9780125850032 |
| language | English |
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| physical | XV, 463 S. graph. Darst. |
| publishDate | 2003 |
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| spelling | Reed, Michael 1942- Verfasser (DE-588)121352889 aut Methods of modern mathematical physics 3 Scattering theory Michael Reed ; Barry Simon [Nachdr.] New York [u.a.] Acad. Press 2003 XV, 463 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Simon, Barry 1946- Verfasser (DE-588)134200195 aut (DE-604)BV002367875 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014583863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reed, Michael 1942- Simon, Barry 1946- Methods of modern mathematical physics |
| title | Methods of modern mathematical physics |
| title_auth | Methods of modern mathematical physics |
| title_exact_search | Methods of modern mathematical physics |
| title_exact_search_txtP | Methods of modern mathematical physics |
| title_full | Methods of modern mathematical physics 3 Scattering theory Michael Reed ; Barry Simon |
| title_fullStr | Methods of modern mathematical physics 3 Scattering theory Michael Reed ; Barry Simon |
| title_full_unstemmed | Methods of modern mathematical physics 3 Scattering theory Michael Reed ; Barry Simon |
| title_short | Methods of modern mathematical physics |
| title_sort | methods of modern mathematical physics scattering theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014583863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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