Schrödinger equations and diffusion theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel u.a.
Birkhäuser
1993
|
| Series: | Monographs in mathematics
86 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | 319 S. graph. Darst. |
| ISBN: | 3764328754 0817628754 9783034805599 |
Staff View
MARC
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| 100 | 1 | |a Nagasawa, Masao |d 1933- |e Verfasser |0 (DE-588)172577640 |4 aut | |
| 245 | 1 | 0 | |a Schrödinger equations and diffusion theory |c Masao Nagasawa |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1993 | |
| 300 | |a 319 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs in mathematics |v 86 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Processus de diffusion |2 ram | |
| 650 | 7 | |a Schrödinger, équation de |2 ram | |
| 650 | 4 | |a Diffusion processes | |
| 650 | 4 | |a Schrödinger equation | |
| 650 | 0 | 7 | |a Schrödinger-Gleichung |0 (DE-588)4053332-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diffusionsgleichung |0 (DE-588)4149816-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diffusionsprozess |0 (DE-588)4274463-5 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804121438181916672 |
|---|---|
| adam_text | Contents
Preface
хд
Chapter I
Introduction and Motivation
1.1
Quantization
1
1.2
Schrodinger Equation
2
1.3
Quantum Mechanics and Diffusion Processes
4
1.4
Equivalence of Schrodinger and Diffusion Equations
6
1.5
Time Reversal and Duality
7
1.6
QED and Quantum Field Theory
9
1.7
What is the Schrodinger Equation
? 10
1.8
Mathematical Contents
12
Chapter II
Diffusion Processes and their Transformations
2.1
Time-Homogeneous Diffusion Processes
13
2.2
Time-Inhomogeneous Diffusion Processes
17
2.3
Brownian Motions
19
2.4
Stochastic Differential Equations
21
2.5
Transformation by a Multiplicative Functional
27
2.6
Feynman-Kac Formula
31
2.7
Kac s Semi-Group and its Renormalization
33
2.8
TimeChimge
37
2.9
Dirichlet Problem
40
2.10
Feller s One-Dimensional Diffusion Processes
42
2.11
Feller s Test
46
vi
Contents
Chapter
III
Duality and Time Reversal of
Diffusion Processes
3.1
Kolmogoroff
s
Duality
55
3.2
Time Reversal of Diffusion Processes
63
3.3
Duality of Time-Inhomogeneous Diffusion Processes
69
3.4 Schrödinger s
and Kolmogoroff
s
Representations
75
3.5
Some Remarks
86
Chapter IV
Equivalence of Diffusion and
Schrodinger Equations
4.1
Change of Variables Formulae
89
4.2
Equivalence Theorem
94
4.3
Discussion of the Non-Linear Dependence
96
4.4
A Solution to
Schrödinger s
Conjecture
100
4.5
A Unified Theory
101
4.6
On Quantization
104
4.7
As a Diffusion Theory
107
4.8
Principle of Superposition
108
4.9
Remarks
П4
Chapter V
Variational Principle
5.1
Problem Setting in the /^-Representation
115
5.2
Csiszar s Projection Theorem
118
5.3
Reference Processes
119
5.4
Diffusion Processes in
Schrödinger s
Representation
125
5.5
Weak Fundamental Solutions
131
5.6
An Entropy Characterization of the Markov Property
132
5.7
Remarks
135
Contents
vii
Chapter VI
Diffusion Processes in ^-Representation
6.1
A Multiplicative Functional
139
6.2
Flows of Distribution Densities
146
6.3
Discussions on the ^-Representation
149
6.4
What is the Feynman Iotegral
? 152
6.5
A Remark on Kac s Semi-Group
156
6.6
A Typical Case
159
6.7
Hydrogen Atom
160
6.8
A Remark on
{μα,
ßb] 161
Chapter
VII
Segregation of a Population
7.1
Introduction
163
7.2
Harmonic Oscillator
164
7.3
Segregation of a Finite-System of Particles
166
7.4
A Formulation of the Propagation of Chaos
170
7.5
The Propagation of Chaos
171
7.6
Skorokhod s Problem with Singular Drift
174
7.7
A Limit Theorem
185
7.8
A Proof of Theorem
7.1 195
7.9
Schrodmger Equations with Singular Potentials
198
Chapter
The
Schrödinger
Equation can
be a Boltzmann Equation
8.1
Large Deviations
207
8.2
The Propagation of Chaos in Terms of Large Deviations
215
8.3
Statistical Mechanics for
Schrödinger
Equations
219
8.4
Some Comments
221
viii Contents
Chapter IX
Applications of the Statistical Model
for
Schrödinger
Equations
9.1
Segregation of a Monkey Population
223
9.2
An Eigenvalue Problem
226
9.3
Septation of Escherichia
Coli
227
9.4
The Mass Spectrum of Mesons
233
9.5
Titius-Bode Law
238
Chapter X
Relative Entropy and Csiszar s Projection
10.1
Relative Entropy
239
10.2
Csiszar s Projection
243
10.3
Exponential Families and Marginal Distributions
246
Chapter XI
Large Deviations
11.1
Lemmas
253
11.2
Large Deviations of Empirical Distributions
255
Chapter
ХП
Non-Linearity Induced by
the Branching Property
12.1
Branching Property
261
12.2
Non-Linear Equations of Branching Processes
265
12.3
Quasi-Linear Parabolic Equations
268
12.4
Branching Markov Processes with Non-Linear Drift
272
12.5
Revival of a Markov Process
273
12.6
Construction of Branching Markov Processes
276
Contents ix
Appendix:
a.l
Fényes
Equation
of
Motion
of Probability Densities
281
a,2
Stochastic Mechanics
283
а.З
Segregation of a Population
287
a.4 Euclidean Quantum Mechanics
288
a.5 Remarks
290
a.6 Bohmian Mechanics
291
References
295
Index
311
|
| any_adam_object | 1 |
| author | Nagasawa, Masao 1933- |
| author_GND | (DE-588)172577640 |
| author_facet | Nagasawa, Masao 1933- |
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| dewey-full | 519.2/33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 |
| dewey-search | 519.2/33 |
| dewey-sort | 3519.2 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-09T16:57:59Z |
| institution | BVB |
| isbn | 3764328754 0817628754 9783034805599 |
| language | English |
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| physical | 319 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Nagasawa, Masao 1933- Verfasser (DE-588)172577640 aut Schrödinger equations and diffusion theory Masao Nagasawa Basel u.a. Birkhäuser 1993 319 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics 86 Hier auch später erschienene, unveränderte Nachdrucke Processus de diffusion ram Schrödinger, équation de ram Diffusion processes Schrödinger equation Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Diffusionsgleichung (DE-588)4149816-1 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 s Diffusionsgleichung (DE-588)4149816-1 s DE-604 Diffusionsprozess (DE-588)4274463-5 s Monographs in mathematics 86 (DE-604)BV000008284 86 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004627842&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nagasawa, Masao 1933- Schrödinger equations and diffusion theory Monographs in mathematics Processus de diffusion ram Schrödinger, équation de ram Diffusion processes Schrödinger equation Schrödinger-Gleichung (DE-588)4053332-3 gnd Diffusionsgleichung (DE-588)4149816-1 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| subject_GND | (DE-588)4053332-3 (DE-588)4149816-1 (DE-588)4274463-5 |
| title | Schrödinger equations and diffusion theory |
| title_auth | Schrödinger equations and diffusion theory |
| title_exact_search | Schrödinger equations and diffusion theory |
| title_full | Schrödinger equations and diffusion theory Masao Nagasawa |
| title_fullStr | Schrödinger equations and diffusion theory Masao Nagasawa |
| title_full_unstemmed | Schrödinger equations and diffusion theory Masao Nagasawa |
| title_short | Schrödinger equations and diffusion theory |
| title_sort | schrodinger equations and diffusion theory |
| topic | Processus de diffusion ram Schrödinger, équation de ram Diffusion processes Schrödinger equation Schrödinger-Gleichung (DE-588)4053332-3 gnd Diffusionsgleichung (DE-588)4149816-1 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| topic_facet | Processus de diffusion Schrödinger, équation de Diffusion processes Schrödinger equation Schrödinger-Gleichung Diffusionsgleichung Diffusionsprozess |
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