Intermediate spectral theory and quantum dynamics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel
Birkhäuser
2009
|
| Series: | Progress in Mathematical Physics
54 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 410 S. |
| ISBN: | 9783764387952 9783764387945 |
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| adam_text | CONTENTS PREFACE XI SELECTED NOTATION XV A GLANCE AT QUANTUM MECHANICS 1
1 LINEAR OPERATORS AND SPECTRA 1.1 BOUNDED OPERATORS 5 1.2 CLOSED
OPERATORS 15 1.3 COMPACT OPERATORS 20 1.4 HUBERT-SCHMIDT OPERATORS 27
1.5 THE SPECTRUM 32 1.6 SPECTRA OF COMPACT OPERATORS 39 2 ADJOINT
OPERATOR 2.1 ADJOINT OPERATOR 43 2.2 CAYLEY TRANSFORM I 49 2.3 EXAMPLES
54 2.3.1 MOMENTUM AND ENERGY 54 2.3.2 MULTIPLICATION OPERATOR 62 2.4
WEYL SEQUENCES 64 2.5 CAYLEY TRANSFORM II 68 2.6 EXAMPLES 73 3 FOURIER
TRANSFORM AND FVEE HAMILTONIAN 3.1 FOURIER TRANSFORM 79 3.2 SOBOLEV
SPACES 82 3.3 MOMENTUM OPERATOR 89 3.4 KINETIC ENERGY AND FREE PARTICLE
90 3.4.1 FREE RESOLVENT 92 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/989188477 DIGITALISIERT DURCH 7.5.1 A MULTIPLY
CONNECTED DOMAIN 195 [ CONTENTS OPERATORS VIA SESQUILINEAR FORMS 4.1
SESQUILINEAR FORMS 95 4.2 OPERATORS ASSOCIATED WITH FORMS 100 4.3
FRIEDRICHS EXTENSION 107 4.4 EXAMPLES 111 4.4.1 HARDY S INEQUALITY 118
UNITARY EVOLUTION GROUPS 5.1 UNITARY EVOLUTION GROUPS 121 5.2 BOUNDED
INFINITESIMAL GENERATORS 126 5.3 STONE THEOREM 129 5.4 EXAMPLES 132 5.5
FREE QUANTUM DYNAMICS 137 5.5.1 HEAT EQUATION 141 5.6 TROTTER PRODUCT
FORMULA 142 KATO-RELLICH THEOREM 6.1 RELATIVELY BOUNDED PERTURBATIONS
145 6.1.1 KLMN THEOREM 149 6.2 APPLICATIONS 150 6.2.1 H-ATOM AND VIRIAL
THEOREM 150 6.2.2 KLMN: APPLICATIONS 155 6.2.3 SOME LF OC (R N )
POTENTIALS 158 6.3 KATO S INEQUALITY AND POINTWISE POSITIVITY 161
BOUNDARY TRIPLES AND SELF-ADJOINTNESS 7.1 BOUNDARY FORMS 169 7.1.1
BOUNDARY TRIPLES 172 7.2 SCHROEDINGER OPERATORS ON INTERVALS 174 7.2.1
REGULAER AND SINGULAR END POINTS 175 7.2.2 LIMIT POINT, LIMIT CIRCLE 178
7.3 REGULAER EXAMPLES 181 7.4 SINGULAR EXAMPLES AND ALL THAT 184 7.4.1
ONE-DIMENSIONAL H-ATOM 185 7.4.2 SOME POINT INTERACTIONS 188 7.5
SPHERICALLY SYMMETRIE POTENTIALS 192 CONTENTS IX 8 SPECTRAL THEOREM 8.1
COMPACT SELF-ADJOINT OPERATORS 201 8.1.1 COMPACT NORMAL OPERATORS 204
8.2 RESOLUTION OF THE IDENTITY 205 8.3 SPECTRAL THEOREM 211 8.4 EXAMPLES
219 8.4.1 MULTIPLICATION OPERATOR 219 8.4.2 PURELY POINT OPERATORS 223
8.4.3 TIGHT-BINDING KINETIC ENERGY 224 8.5 COMMENTS ON PROOFS 225 9
APPLICATIONS OF THE SPECTRAL THEOREM 9.1 QUANTUM INTERPRETATION OF
SPECTRAL MEASURES 229 9.2 PROOF OF THEOREM 5.3.1 230 9.3 FORM DOMAIN OF
POSITIVE OPERATORS 231 9.3.1 DOMAIN OF FORM SUM OF OPERATORS 236 9.4
POLAR DECOMPOSITION 238 9.4.1 TRACE-CLASS OPERATORS 239 9.5 MISCELLANEA
242 9.6 SPECTRAL MAPPING 248 9.7 DUHAMEL FORMULA 249 9.8 REDUCING
SUBSPACES 250 9.9 SEQUENCES AND EVOLUTION GROUPS 254 10 CONVERGENCE OF
SELF-ADJOINT OPERATORS 10.1 RESOLVENT AND DYNAMICAL CONVERGENCES 257
10.2 RESOLVENT CONVERGENCE AND SPECTRUM 264 10.3 EXAMPLES 266 10.3.1
NONRELATIVISTIC LIMIT OF DIRAC OPERATOR 269 10.4 SESQUILINEAR FORM
CONVERGENCE 271 10.4.1 NONDECREASING SEQUENCES 271 10.4.2 NONINCREASING
SEQUENCES 276 10.5 APPLICATION TO THE AHARONOV-BOHM EFFECT 279 11
SPECTRAL DECOMPOSITION I 11.1 SPECTRAL REDUCTION 283 11.2 DISCRETE AND
ESSENTIAL SPECTRA 285 11.3 ESSENTIAL SPECTRUM AND COMPACT PERTURBATIONS
289 11.3. X CONTENTS 11.4.3 THREE SIMPLE CLASSES OF POTENTIALS 298
11.4.4 EXISTENCE OF NEGATIVE EIGENVALUES 300 11.4.5 RESOLVENT
CONVERGENCE AND ESSENTIAL SPECTRUM 303 11.5 DISCRETE SPECTRUM FOR
UNBOUNDED POTENTIALS 305 11.6 SPECTRA OF SELF-ADJOINT EXTENSIONS 307
11.6.1 GREEN FUNCTION AND A FREE COMPACT RESOLVENT 310 12 SPECTRAL
DECOMPOSITION II 12.1 POINT, ABSOLUTELY CONTINUOUS AND SINGULAR
CONTINUOUS SUBSPACES 313 12.2 EXAMPLES 318 12.3 SOME ABSOLUTELY
CONTINUOUS SPECTRA 324 12.3.1 MULTIPLICATION OPERATORS 324 12.3.2 PUTNAM
COMMUTATOR THEOREM 326 12.3.3 SCATTERING AND KATO-ROSENBLUM THEOREM 331
12.4 MAGNETIC FIELD: LANDAU LEVELS 337 12.4.1 MAGNETIC RESOLVENT
CONVERGENCE 342 12.5 WEYL-VON NEUMANN THEOREM 343 12.6 WONDERLAND
THEOREM 348 13 SPECTRUM AND QUANTUM DYNAMICS 13.1 POINT SUBSPACE:
PRECOMPACT ORBITS 353 13.2 ALMOST PERIODIC TRAJECTORIES 356 13.3 QUANTUM
RETURN PROBABILITY 358 13.4 RAGE THEOREM AND TEST OPERATORS 363 13.5
CONTINUOUS SUBSPACE: RETURN PROBABILITY DECAY 365 13.6 BOUND AND
SCATTERING STATES IN R 369 13.7 A-HOELDER SPECTRAL MEASURES 374 14 SOME
QUANTUM RELATIONS 14.1 HERMITIAN X SELF-ADJOINT OPERATORS 379 14.2
UNCERTAINTY PRINCIPLE 381 14.3 COMMUTING OBSERVABLES 384 14.4
PROBABILITY CURRENT 388 14.5 EHRENFEST THEOREM 392 BIBLIOGRAPHY 39
|
| adam_txt |
CONTENTS PREFACE XI SELECTED NOTATION XV A GLANCE AT QUANTUM MECHANICS 1
1 LINEAR OPERATORS AND SPECTRA 1.1 BOUNDED OPERATORS 5 1.2 CLOSED
OPERATORS 15 1.3 COMPACT OPERATORS 20 1.4 HUBERT-SCHMIDT OPERATORS 27
1.5 THE SPECTRUM 32 1.6 SPECTRA OF COMPACT OPERATORS 39 2 ADJOINT
OPERATOR 2.1 ADJOINT OPERATOR 43 2.2 CAYLEY TRANSFORM I 49 2.3 EXAMPLES
54 2.3.1 MOMENTUM AND ENERGY 54 2.3.2 MULTIPLICATION OPERATOR 62 2.4
WEYL SEQUENCES 64 2.5 CAYLEY TRANSFORM II 68 2.6 EXAMPLES 73 3 FOURIER
TRANSFORM AND FVEE HAMILTONIAN 3.1 FOURIER TRANSFORM 79 3.2 SOBOLEV
SPACES 82 3.3 MOMENTUM OPERATOR 89 3.4 KINETIC ENERGY AND FREE PARTICLE
90 3.4.1 FREE RESOLVENT 92 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/989188477 DIGITALISIERT DURCH 7.5.1 A MULTIPLY
CONNECTED DOMAIN 195 [ CONTENTS OPERATORS VIA SESQUILINEAR FORMS 4.1
SESQUILINEAR FORMS 95 4.2 OPERATORS ASSOCIATED WITH FORMS 100 4.3
FRIEDRICHS EXTENSION 107 4.4 EXAMPLES 111 4.4.1 HARDY'S INEQUALITY 118
UNITARY EVOLUTION GROUPS 5.1 UNITARY EVOLUTION GROUPS 121 5.2 BOUNDED
INFINITESIMAL GENERATORS 126 5.3 STONE THEOREM 129 5.4 EXAMPLES 132 5.5
FREE QUANTUM DYNAMICS 137 5.5.1 HEAT EQUATION 141 5.6 TROTTER PRODUCT
FORMULA 142 KATO-RELLICH THEOREM 6.1 RELATIVELY BOUNDED PERTURBATIONS
145 6.1.1 KLMN THEOREM 149 6.2 APPLICATIONS 150 6.2.1 H-ATOM AND VIRIAL
THEOREM 150 6.2.2 KLMN: APPLICATIONS 155 6.2.3 SOME LF OC (R N )
POTENTIALS 158 6.3 KATO'S INEQUALITY AND POINTWISE POSITIVITY 161
BOUNDARY TRIPLES AND SELF-ADJOINTNESS 7.1 BOUNDARY FORMS 169 7.1.1
BOUNDARY TRIPLES 172 7.2 SCHROEDINGER OPERATORS ON INTERVALS 174 7.2.1
REGULAER AND SINGULAR END POINTS 175 7.2.2 LIMIT POINT, LIMIT CIRCLE 178
7.3 REGULAER EXAMPLES 181 7.4 SINGULAR EXAMPLES AND ALL THAT 184 7.4.1
ONE-DIMENSIONAL H-ATOM 185 7.4.2 SOME POINT INTERACTIONS 188 7.5
SPHERICALLY SYMMETRIE POTENTIALS 192 CONTENTS IX 8 SPECTRAL THEOREM 8.1
COMPACT SELF-ADJOINT OPERATORS 201 8.1.1 COMPACT NORMAL OPERATORS 204
8.2 RESOLUTION OF THE IDENTITY 205 8.3 SPECTRAL THEOREM 211 8.4 EXAMPLES
219 8.4.1 MULTIPLICATION OPERATOR 219 8.4.2 PURELY POINT OPERATORS 223
8.4.3 TIGHT-BINDING KINETIC ENERGY 224 8.5 COMMENTS ON PROOFS 225 9
APPLICATIONS OF THE SPECTRAL THEOREM 9.1 QUANTUM INTERPRETATION OF
SPECTRAL MEASURES 229 9.2 PROOF OF THEOREM 5.3.1 230 9.3 FORM DOMAIN OF
POSITIVE OPERATORS 231 9.3.1 DOMAIN OF FORM SUM OF OPERATORS 236 9.4
POLAR DECOMPOSITION 238 9.4.1 TRACE-CLASS OPERATORS 239 9.5 MISCELLANEA
242 9.6 SPECTRAL MAPPING 248 9.7 DUHAMEL FORMULA 249 9.8 REDUCING
SUBSPACES 250 9.9 SEQUENCES AND EVOLUTION GROUPS 254 10 CONVERGENCE OF
SELF-ADJOINT OPERATORS 10.1 RESOLVENT AND DYNAMICAL CONVERGENCES 257
10.2 RESOLVENT CONVERGENCE AND SPECTRUM 264 10.3 EXAMPLES 266 10.3.1
NONRELATIVISTIC LIMIT OF DIRAC OPERATOR 269 10.4 SESQUILINEAR FORM
CONVERGENCE 271 10.4.1 NONDECREASING SEQUENCES 271 10.4.2 NONINCREASING
SEQUENCES 276 10.5 APPLICATION TO THE AHARONOV-BOHM EFFECT 279 11
SPECTRAL DECOMPOSITION I 11.1 SPECTRAL REDUCTION 283 11.2 DISCRETE AND
ESSENTIAL SPECTRA 285 11.3 ESSENTIAL SPECTRUM AND COMPACT PERTURBATIONS
289 11.3. X CONTENTS 11.4.3 THREE SIMPLE CLASSES OF POTENTIALS 298
11.4.4 EXISTENCE OF NEGATIVE EIGENVALUES 300 11.4.5 RESOLVENT
CONVERGENCE AND ESSENTIAL SPECTRUM 303 11.5 DISCRETE SPECTRUM FOR
UNBOUNDED POTENTIALS 305 11.6 SPECTRA OF SELF-ADJOINT EXTENSIONS 307
11.6.1 GREEN FUNCTION AND A FREE COMPACT RESOLVENT 310 12 SPECTRAL
DECOMPOSITION II 12.1 POINT, ABSOLUTELY CONTINUOUS AND SINGULAR
CONTINUOUS SUBSPACES 313 12.2 EXAMPLES 318 12.3 SOME ABSOLUTELY
CONTINUOUS SPECTRA 324 12.3.1 MULTIPLICATION OPERATORS 324 12.3.2 PUTNAM
COMMUTATOR THEOREM 326 12.3.3 SCATTERING AND KATO-ROSENBLUM THEOREM 331
12.4 MAGNETIC FIELD: LANDAU LEVELS 337 12.4.1 MAGNETIC RESOLVENT
CONVERGENCE 342 12.5 WEYL-VON NEUMANN THEOREM 343 12.6 WONDERLAND
THEOREM 348 13 SPECTRUM AND QUANTUM DYNAMICS 13.1 POINT SUBSPACE:
PRECOMPACT ORBITS 353 13.2 ALMOST PERIODIC TRAJECTORIES 356 13.3 QUANTUM
RETURN PROBABILITY 358 13.4 RAGE THEOREM AND TEST OPERATORS 363 13.5
CONTINUOUS SUBSPACE: RETURN PROBABILITY DECAY 365 13.6 BOUND AND
SCATTERING STATES IN R" 369 13.7 A-HOELDER SPECTRAL MEASURES 374 14 SOME
QUANTUM RELATIONS 14.1 HERMITIAN X SELF-ADJOINT OPERATORS 379 14.2
UNCERTAINTY PRINCIPLE 381 14.3 COMMUTING OBSERVABLES 384 14.4
PROBABILITY CURRENT 388 14.5 EHRENFEST THEOREM 392 BIBLIOGRAPHY 39 |
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| dewey-sort | 3530.12 |
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| discipline_str_mv | Physik Mathematik |
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| id | DE-604.BV035193129 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T23:02:17Z |
| indexdate | 2024-07-09T21:27:08Z |
| institution | BVB |
| isbn | 9783764387952 9783764387945 |
| language | English |
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| physical | XIII, 410 S. |
| publishDate | 2009 |
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| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in Mathematical Physics |
| series2 | Progress in Mathematical Physics |
| spelling | Oliveira, César R. de Verfasser aut Intermediate spectral theory and quantum dynamics César R. de Oliveira Basel Birkhäuser 2009 XIII, 410 S. txt rdacontent n rdamedia nc rdacarrier Progress in Mathematical Physics 54 Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Selbstadjungierter Operator (DE-588)4180810-1 gnd rswk-swf Selbstadjungierter Operator (DE-588)4180810-1 s Spektraltheorie (DE-588)4116561-5 s Quantenmechanik (DE-588)4047989-4 s DE-604 Progress in Mathematical Physics 54 (DE-604)BV013823265 54 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016999710&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Oliveira, César R. de Intermediate spectral theory and quantum dynamics Progress in Mathematical Physics Quantenmechanik (DE-588)4047989-4 gnd Spektraltheorie (DE-588)4116561-5 gnd Selbstadjungierter Operator (DE-588)4180810-1 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4116561-5 (DE-588)4180810-1 |
| title | Intermediate spectral theory and quantum dynamics |
| title_auth | Intermediate spectral theory and quantum dynamics |
| title_exact_search | Intermediate spectral theory and quantum dynamics |
| title_exact_search_txtP | Intermediate spectral theory and quantum dynamics |
| title_full | Intermediate spectral theory and quantum dynamics César R. de Oliveira |
| title_fullStr | Intermediate spectral theory and quantum dynamics César R. de Oliveira |
| title_full_unstemmed | Intermediate spectral theory and quantum dynamics César R. de Oliveira |
| title_short | Intermediate spectral theory and quantum dynamics |
| title_sort | intermediate spectral theory and quantum dynamics |
| topic | Quantenmechanik (DE-588)4047989-4 gnd Spektraltheorie (DE-588)4116561-5 gnd Selbstadjungierter Operator (DE-588)4180810-1 gnd |
| topic_facet | Quantenmechanik Spektraltheorie Selbstadjungierter Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016999710&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013823265 |
| work_keys_str_mv | AT oliveiracesarrde intermediatespectraltheoryandquantumdynamics |