Mathematical methods in quantum mechanics: with applications to Schrödinger operators
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2014
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate studies in mathematics
157 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 358 S. graph. Darst. |
| ISBN: | 9781470417048 |
Internformat
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| 245 | 1 | 0 | |a Mathematical methods in quantum mechanics |b with applications to Schrödinger operators |c Gerald Teschl |
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Datensatz im Suchindex
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| adam_text | Titel: Mathematical methods in quantum mechanics
Autor: Teschl, Gerald
Jahr: 2014
Contents Preface Part 0. Preliminaries Chapter 0. A first look at Banach and Hilbert spaces §0.1. Warm up: Metric and topological spaces §0.2. The Banach space of continuous functions §0.3. The geometry of Hilbert spaces §0.4. Completeness §0.5. Bounded operators §0.6. Lebesgue L p spaces §0.7. Appendix: The uniform boundedness principle Part 1. Mathematical Foundations of Quantum Mechanics Chapter 1. Hilbert spaces §1.1. Hilbert spaces §1.2. Orthonormal bases §1.3. The projection theorem and the Riesz lemma §1.4. Orthogonal sums and tensor products §1.5. The C* algebra of bounded linear operators §1.6. Weak and strong convergence §1.7. Appendix: The Stone-Weierstrafi theorem Chapter 2. Self-adjointness and spectrum xi 3 3 14 21 26 27 30 38 43 43 45 49 52 54 55 59 63
Contents viii §2.1. Some quantum mechanics 63 §2.2. Self-adjoint operators 66 §2.3. Quadratic forms and the Friedrichs extension 76 §2.4. Resolvents and spectra 83 §2.5. Orthogonal sums of operators 89 §2.6. Self-adjoint extensions 91 §2.7. Appendix: Absolutely continuous functions 95 Chapter 3. The spectral theorem 99 §3.1. The spectral theorem 99 §3.2. More on Borel measures 112 §3.3. Spectral types 118 §3.4. Appendix: Herglotz-Nevanlinna functions 120 Chapter 4. Applications of the spectral theorem 131 §4.1. Integral formulas 131 §4.2. Commuting operators 135 §4.3. Polar decomposition 138 §4.4. The min-max theorem 140 §4.5. Estimating eigenspaces 142 §4.6. Tensor products of operators 143 Chapter 5. Quantum dynamics 145 §5.1. The time evolution and Stone’s theorem 145 §5.2. The RAGE theorem 150 §5.3. The Trotter product formula 155 Chapter 6. Perturbation theory for self-adjoint operators 157 §6.1. Relatively bounded operators and the Kato-Rellich theorem 157 §6.2. More on compact operators 160 §6.3. Hilbert-Schmidt and trace class operators 163 §6.4. Relatively compact operators and Weyl’s theorem 170 §6.5. Relatively form-bounded operators and the KLMN theorem 174 §6.6. Strong and norm resolvent convergence 179 Part 2. Schrödinger Operators Chapter 7. The free Schrödinger operator 187 §7.1. The Fourier transform 187
Contents ix §7.2. Sobolev spaces 194 §7.3. The free Sclirodinger operator 197 §7.4. The time evolution in the free case 199 §7.5. The resolvent and Green’s function 201 Chapter 8. Algebraic methods 207 §8.1. Position and momentum 207 §8.2. Angular momentum 209 §8.3. The harmonic oscillator 212 §8.4. Abstract commutation 214 Chapter 9. One-dimensional Sclirodinger operators 217 §9.1. Sturm-Liouville operators 217 §9.2. Weyl’s limit circle, limit point alternative 223 §9.3. Spectral transformations I 231 §9.4. Inverse spectral theory 238 §9.5. Absolutely continuous spectrum 242 §9.6. Spectral transformations II 245 §9.7. The spectra of one-dimensional Sclirodinger operators 250 Chapter 10. One-particle Sclirodinger operators 257 §10.1. Self-adjointness and spectrum 257 §10.2. The hydrogen atom 258 §10.3. Angular momentum 261 §10.4. The eigenvalues of the hydrogen atom 265 §10.5. Nondegeneracy of the ground state 272 Chapter 11. Atomic Sclirodinger operators 275 §11.1. Self-adjointness 275 §11.2. The HVZ theorem 278 Chapter 12. Scattering theory 283 §12.1. Abstract theory 283 §12.2. Incoming and outgoing states 286 §12.3. Sclirodinger operators with short range potentials 289 Part 3. Appendix Appendix A. Almost everything about Lebesgue integration 295 §A.l. Borel measures in a nutshell 295
X Contents §A.2. Extending a premeasure to a measure 303 §A.3. Measurable functions 307 §A.4. How wild are measurable objects? 309 §A.5. Integration — Sum me up, Henri 312 §A.6. Product measures 319 §A.7. Transformation of measures and integrals 322 §A.8. Vague convergence of measures 328 §A.9. Decomposition of measures 331 §A.10. Derivatives of measures 334 Bibliographical notes 341 Bibliography 345 Glossary of notation 349 Index 353
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| dewey-full | 515.724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.724 |
| dewey-search | 515.724 |
| dewey-sort | 3515.724 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | 2. ed. |
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| isbn | 9781470417048 |
| language | English |
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| spelling | Teschl, Gerald 1970- Verfasser (DE-588)140501037 aut Mathematical methods in quantum mechanics with applications to Schrödinger operators Gerald Teschl 2. ed. Providence, RI American Math. Soc. 2014 XIV, 358 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 157 Quantentheorie (DE-588)4047992-4 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 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 978-1-4704-1888-5 Graduate studies in mathematics 157 (DE-604)BV009739289 157 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027456146&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 Quantentheorie (DE-588)4047992-4 gnd Hamilton-Operator (DE-588)4072278-8 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4072278-8 (DE-588)4155620-3 |
| 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 | Quantentheorie (DE-588)4047992-4 gnd Hamilton-Operator (DE-588)4072278-8 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Quantentheorie Hamilton-Operator Mathematische Methode |
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