From Brownian motion to Schrödinger's equation:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1995
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
312 |
| Schlagworte: | |
| Online-Zugang: | Table of contents only Publisher description Inhaltsverzeichnis |
| Beschreibung: | XII, 287 S. graph. Darst. |
| ISBN: | 3540570306 0387570306 |
Internformat
MARC
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| 245 | 1 | 0 | |a From Brownian motion to Schrödinger's equation |c Kai Lai Chung ; Zhongxin Zhao |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1995 | |
| 300 | |a XII, 287 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804124499357990912 |
|---|---|
| adam_text | Table of Contents
1. Preparatory Material 1
1.1 Basic Notation 1
1.2 Markov Process and Strong Markov Property 3
1.3 Construction of Brownian Motion 9
1.4 Harmonic Function and Poisson Kernel 13
1.5 Exit Time and Place 19
1.6 Dirichlet Boundary Value Problem 23
Appendix to Chapter 1 27
Notes on Chapter 1 28
2. Killed Brownian Motion 31
2.1 Feller Properties 31
2.2 Transition Density 33
2.3 Green Potential and Function 37
2.4 Compactness and Spectrum 46
2.5 Laplacian as Generator 48
Notes on Chapter 2 59
3. Schrodinger Operator 61
3.1 The Schrodinger Equation and Class 3 61
3.2 Semigroup with Multiplicative Functional 71
3.3 Potential Operator and its Inverse 81
3.4 Schrodinger Infinitesimal Generator 88
Notes on Chapter 3 101
4. Stopped Feynman—Kac Functional 103
4.1 Harnack Inequality and Gauge Theorem 103
4.2 Properties of ?d 7 107
4.3 Fundamental Properties of the Gauge 112
4.4 Dirichlet Boundary Value Problem for the Schrodinger Equation . 114
4.5 Representation Theorem 117
4.6 Equivalence Theorem for Gaugeability 124
Notes on Chapter 4 128
XII Table of Contents
5. Conditional Brownian Motion and Conditional Gauge 131
5.1 Conditional Brownian Motion 131
5.2 Life in a Lipschitz Domain 135
5.3 Conditional Gauge for a Small Ball 144
5.4 General Gauge Theorem 149
5.5 Continuity of Weak Solutions 152
5.6 New Approach to the Gauge Theorem 155
Notes on Chapter 5 157
6. Green Functions 159
6.1 Basic Properties of the gr-Green Function 159
6.2 Inequalites for Green Functions in a Lipschitz Domain
in Rd (d 3) 163
6.3 Inequalities for Green Functions in a Jordan Domain in R2 175
Notes on Chapter 6 190
7. Conditional Gauge and g-Green Function 191
7.1 Conditional Gauge Theorem 191
7.2 Approximation and Continuity of the Conditional Gauge 197
7.3 Extended Conditional Gauge Theorem 200
7.4 Representation of the Conditional Gauge 207
Notes on Chapter 7 213
8. Various Related Developments 215
8.1 Variation of Gauge 215
8.2 Variation of the Principal Eigenvalue 220
8.3 Principal Eigenfunction and Sharp Variation 224
8.4 Boundary Harnack Principle and Application 230
8.5 Schrodinger Equation in the Classical Setting 234
8.6 Dirichlet Problem and Truncated Gauge 236
Notes on Chapter 8 239
9. The Case of One Dimension 241
9.1 Fundamental Expectations 241
9.2 Gauge for a Finite or Infinite Interval 248
9.3 Special Cases and Examples 262
9.4 Local Time and Density 270
9.5 Derivatives and Neumann s Problem 274
Notes on Chapter 9 278
References 281
Index 285
|
| any_adam_object | 1 |
| author | Chung, Kai Lai 1917-2009 Zhao, Zhongxin 1942- |
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| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV010107499 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:46:38Z |
| institution | BVB |
| isbn | 3540570306 0387570306 |
| language | English |
| lccn | 95001414 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006711111 |
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| physical | XII, 287 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
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| publisher | Springer |
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| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Chung, Kai Lai 1917-2009 Verfasser (DE-588)136125484 aut From Brownian motion to Schrödinger's equation Kai Lai Chung ; Zhongxin Zhao Berlin [u.a.] Springer 1995 XII, 287 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 312 Brownse beweging gtt Mouvement brownien, Processus de Mouvement brownien, processus de ram Schrödinger, Équation de Schrödinger, équation de ram Schrödingervergelijking gtt Schrödinger equation Brownian motion processes Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 s DE-604 Brownsche Bewegung (DE-588)4128328-4 s Markov-Prozess (DE-588)4134948-9 s Zhao, Zhongxin 1942- Verfasser (DE-588)1011691558 aut Grundlehren der mathematischen Wissenschaften 312 (DE-604)BV000000395 312 text/html http://www.loc.gov/catdir/enhancements/fy0815/95001414-t.html Table of contents only text/html http://www.loc.gov/catdir/enhancements/fy0815/95001414-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006711111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chung, Kai Lai 1917-2009 Zhao, Zhongxin 1942- From Brownian motion to Schrödinger's equation Grundlehren der mathematischen Wissenschaften Brownse beweging gtt Mouvement brownien, Processus de Mouvement brownien, processus de ram Schrödinger, Équation de Schrödinger, équation de ram Schrödingervergelijking gtt Schrödinger equation Brownian motion processes Schrödinger-Gleichung (DE-588)4053332-3 gnd Markov-Prozess (DE-588)4134948-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd |
| subject_GND | (DE-588)4053332-3 (DE-588)4134948-9 (DE-588)4128328-4 |
| title | From Brownian motion to Schrödinger's equation |
| title_auth | From Brownian motion to Schrödinger's equation |
| title_exact_search | From Brownian motion to Schrödinger's equation |
| title_full | From Brownian motion to Schrödinger's equation Kai Lai Chung ; Zhongxin Zhao |
| title_fullStr | From Brownian motion to Schrödinger's equation Kai Lai Chung ; Zhongxin Zhao |
| title_full_unstemmed | From Brownian motion to Schrödinger's equation Kai Lai Chung ; Zhongxin Zhao |
| title_short | From Brownian motion to Schrödinger's equation |
| title_sort | from brownian motion to schrodinger s equation |
| topic | Brownse beweging gtt Mouvement brownien, Processus de Mouvement brownien, processus de ram Schrödinger, Équation de Schrödinger, équation de ram Schrödingervergelijking gtt Schrödinger equation Brownian motion processes Schrödinger-Gleichung (DE-588)4053332-3 gnd Markov-Prozess (DE-588)4134948-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd |
| topic_facet | Brownse beweging Mouvement brownien, Processus de Mouvement brownien, processus de Schrödinger, Équation de Schrödinger, équation de Schrödingervergelijking Schrödinger equation Brownian motion processes Schrödinger-Gleichung Markov-Prozess Brownsche Bewegung |
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| volume_link | (DE-604)BV000000395 |
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