Mathematical methods in quantum mechanics: with applications to Schrödinger operators
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2009
|
| Schriftenreihe: | Graduate studies in mathematics
99 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 305 S. |
| ISBN: | 9780821846605 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical methods in quantum mechanics |b with applications to Schrödinger operators |c Gerald Teschl |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2009 | |
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Datensatz im Suchindex
| _version_ | 1804139193347080192 |
|---|---|
| adam_text | Titel: Mathematical methods in quantum mechanics
Autor: Teschl, Gerald
Jahr: 2009
Contents
Preface xi
Part 0. Preliminaries
Chapter 0. A first look at Banach and Hilbert spaces 3
§0.1. Warm up: Metric and topological spaces 3
§0.2. The Banach space of continuous functions 12
§0.3. The geometry of Hilbert spaces 16
§0.4. Completeness 22
§0.5. Bounded operators 22
§0.6. Lebesgue IP spaces 25
§0.7. Appendix: The uniform boundedness principle 32
Part 1. Mathematical Foundations of Quantum Mechanics
Chapter 1. Hilbert spaces 37
§1.1. Hilbert spaces 37
§1.2. Orthonormal bases 39
§1.3. The projection theorem and the Riesz lemma 43
§1.4. Orthogonal sums and tensor products 45
§1.5. The C* algebra of bounded linear operators 47
§1.6. Weak and strong convergence 49
§1.7. Appendix: The Stone-Weierstrafi theorem 51
Chapter 2. Self-adjointness and spectrum 55
vii
§2.1. Some quantum mechanics 55
§2.2. Self-adjoint operators 58
§2.3. Quadratic forms and the Friedrichs extension 67
§2.4. Resolvents and spectra 73
§2.5. Orthogonal sums of operators 79
§2.6. Self-adjoint extensions 81
§2.7. Appendix: Absolutely continuous functions 84
Chapter 3. The spectral theorem 87
§3.1. The spectral theorem 87
§3.2. More on Borel measures 99
§3.3. Spectral types 104
§3.4. Appendix: The Herglotz theorem 107
Chapter 4. Applications of the spectral theorem 111
§4.1. Integral formulas 111
§4.2. Commuting operators 115
§4.3. The min-max theorem 117
§4.4. Estimating eigenspaces 119
§4.5. Tensor products of operators 120
Chapter 5. Quantum dynamics 123
§5.1. The time evolution and Stone s theorem 123
§5.2. The RAGE theorem 126
§5.3. The Trotter product formula 131
Chapter 6. Perturbation theory for self-adjoint operators 133
§6.1. Relatively bounded operators and the Kato-Rellich theorem 133
§6.2. More on compact operators 136
§6.3. Hiibert-Schmidt and trace class operators 139
§6.4. Relatively compact operators and Weyl s theorem 145
§6.5. Relatively form bounded operators and the KLMN theorem 149
§6.6. Strong and norm resolvent convergence 153
Part 2. Schrodinger Operators
Chapter 7. The free Schrodinger operator 161
§7.1. The Fourier transform 161
§7.2. The free Schrodinger operator 167
§7.3. The time evolution in the free case 169
§7.4. The resolvent and Green s function 171
Chapter 8. Algebraic methods 173
§8.1. Position and momentum 173
§8.2. Angular momentum 175
§8.3. The harmonic oscillator 178
§8.4. Abstract commutation 179
Chapter 9. One-dimensional Schrodinger operators 181
§9.1. Sturm-Liouville operators 181
§9.2. Weyl s limit circle, limit point alternative 187
§9.3. Spectral transformations I 195
§9.4. Inverse spectral theory 202
§9.5. Absolutely continuous spectrum 206
§9.6. Spectral transformations II 209
§9.7. The spectra of one-dimensional Schrodinger operators 214
Chapter 10. One-particle Schrodinger operators 221
§10.1. Self-adjointness and spectrum 221
§10.2. The hydrogen atom 222
§10.3. Angular momentum 225
§10.4. The eigenvalues of the hydrogen atom 229
§10.5. Nondegeneracy of the ground state 235
Chapter 11. Atomic Schrodinger operators 239
§11.1. Self-adjointness 239
§11.2. The HVZ theorem 242
Chapter 12. Scattering theory 247
§12.1. Abstract theory 247
§12.2. Incoming and outgoing states 250
§12.3. Schrodinger operators with short range potentials 253
Part 3. Appendix
Appendix A. Almost everything about Lebesgue integration 259
§A.l. Borel measures in a nut shell 259
§A.2. Extending a premeasure to a measure 263
§A.3. Measurable functions 268
§A.4. The Lebesgue integral 270
§A.5. Product measures 275
§A.6. Vague convergence of measures 278
§A.7. Decomposition of measures 280
§A.8. Derivatives of measures 282
Bibliographical notes 289
Bibliography 293
Glossary of notation 297
Index 301
|
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| indexdate | 2024-07-09T21:40:11Z |
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| isbn | 9780821846605 |
| language | English |
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| publishDate | 2009 |
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| publisher | American Math. Soc. |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Teschl, Gerald 1970- Verfasser (DE-588)140501037 aut Mathematical methods in quantum mechanics with applications to Schrödinger operators Gerald Teschl Providence, RI American Math. Soc. 2009 XIV, 305 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 99 Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 s Quantentheorie (DE-588)4047992-4 s Mathematische Methode (DE-588)4155620-3 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1838-0 Graduate studies in mathematics 99 (DE-604)BV009739289 99 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017605309&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Teschl, Gerald 1970- Mathematical methods in quantum mechanics with applications to Schrödinger operators Graduate studies in mathematics Mathematische Methode (DE-588)4155620-3 gnd Quantentheorie (DE-588)4047992-4 gnd Hamilton-Operator (DE-588)4072278-8 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4047992-4 (DE-588)4072278-8 |
| title | Mathematical methods in quantum mechanics with applications to Schrödinger operators |
| title_auth | Mathematical methods in quantum mechanics with applications to Schrödinger operators |
| title_exact_search | Mathematical methods in quantum mechanics with applications to Schrödinger operators |
| title_full | Mathematical methods in quantum mechanics with applications to Schrödinger operators Gerald Teschl |
| title_fullStr | Mathematical methods in quantum mechanics with applications to Schrödinger operators Gerald Teschl |
| title_full_unstemmed | Mathematical methods in quantum mechanics with applications to Schrödinger operators Gerald Teschl |
| title_short | Mathematical methods in quantum mechanics |
| title_sort | mathematical methods in quantum mechanics with applications to schrodinger operators |
| title_sub | with applications to Schrödinger operators |
| topic | Mathematische Methode (DE-588)4155620-3 gnd Quantentheorie (DE-588)4047992-4 gnd Hamilton-Operator (DE-588)4072278-8 gnd |
| topic_facet | Mathematische Methode Quantentheorie Hamilton-Operator |
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