A brief introduction to classical, statistical, and quantum mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Courant Inst. of Math. Sciences [u.a.]
2006
|
| Schriftenreihe: | Courant lecture notes in mathematics
13 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | VII, 153 S. graph. Darst. |
| ISBN: | 0821842323 9780821842324 |
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| 100 | 1 | |a Bühler, Oliver |e Verfasser |0 (DE-588)1073308537 |4 aut | |
| 245 | 1 | 0 | |a A brief introduction to classical, statistical, and quantum mechanics |c Oliver Bühler |
| 264 | 1 | |a New York, NY |b Courant Inst. of Math. Sciences [u.a.] |c 2006 | |
| 300 | |a VII, 153 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Courant lecture notes in mathematics |v 13 | |
| 500 | |a Includes bibliographical references and index | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
vii
Chapter
1.
Classical Mechanics of
Discrete Systems
1
1.1.
Elements of Newtonian Mechanics
1
1.2.
Calculus of Variations
7
1.3.
Action Principle
12
1.4.
Legendre Transformation
18
1.5.
Canonical Equations
22
1.6.
Rotating Frames of Reference
26
1.7.
Remarks on
Integrable
Systems and Symmetries
27
1.8.
Phase Space Geometry
28
1.9.
Method of Characteristics
31
1.10.
Hamilton-Jacobi Theory
34
1.11.
Parametrized Curves
40
1.12.
Fermat s Principle
42
Chapter
2.
Wave Mechanics
47
2.1.
From Discrete Particles to Continuous Fields
47
2.2.
The Stretched String
49
2.3.
Canonical Equations
54
2.4.
The Two-Dimensional Wave Equation
55
2.5.
Geometric Wave Theory
58
2.6.
Dispersive Wavetrains
62
2.7.
Wavetrain Examples
67
2.8.
Fermat s Principle for Dispersive Waves
69
Chapter
3.
Statistical Mechanics
73
3.1.
Time and Phase Averaging
74
3.2.
Microcanonical Statistical Mechanics
76
3.3.
Canonical Statistical Mechanics
82
3.4.
Examples of Canonical Mechanics
88
3.5.
Free Energy of Macrostates
91
3.6.
Maximum Entropy Principle
93
3.7.
Variational Approximation Method
96
3.8.
Mean Field Theory
99
3.9.
Phase Transitions
102
3.10.
Numerical Methods
104
vi
CONTENTS
Chapter
4.
Quantum Mechanics
109
4.1.
Specific Heat of Gases
109
4.2.
Fundamentals of Quantum States 111
4.3.
Operators and
Observables
115
4.4.
Amplitude Evolution
117
4.5.
Particle on a Lattice
125
4.6.
Continuous State Space
129
4.7.
Evolution of Expectations and Conservation Laws
134
4.8.
Path Integral Approach to Quantum Mechanics
136
4.9.
Quantum Statistical Mechanics
140
4.10.
A Differential Equation for the Canonical Density Matrix
145
Bibliography
149
Index
151
|
| adam_txt |
Contents
Preface
vii
Chapter
1.
Classical Mechanics of
Discrete Systems
1
1.1.
Elements of Newtonian Mechanics
1
1.2.
Calculus of Variations
7
1.3.
Action Principle
12
1.4.
Legendre Transformation
18
1.5.
Canonical Equations
22
1.6.
Rotating Frames of Reference
26
1.7.
Remarks on
Integrable
Systems and Symmetries
27
1.8.
Phase Space Geometry
28
1.9.
Method of Characteristics
31
1.10.
Hamilton-Jacobi Theory
34
1.11.
Parametrized Curves
40
1.12.
Fermat's Principle
42
Chapter
2.
Wave Mechanics
47
2.1.
From Discrete Particles to Continuous Fields
47
2.2.
The Stretched String
49
2.3.
Canonical Equations
54
2.4.
The Two-Dimensional Wave Equation
55
2.5.
Geometric Wave Theory
58
2.6.
Dispersive Wavetrains
62
2.7.
Wavetrain Examples
67
2.8.
Fermat's Principle for Dispersive Waves
69
Chapter
3.
Statistical Mechanics
73
3.1.
Time and Phase Averaging
74
3.2.
Microcanonical Statistical Mechanics
76
3.3.
Canonical Statistical Mechanics
82
3.4.
Examples of Canonical Mechanics
88
3.5.
Free Energy of Macrostates
91
3.6.
Maximum Entropy Principle
93
3.7.
Variational Approximation Method
96
3.8.
Mean Field Theory
99
3.9.
Phase Transitions
102
3.10.
Numerical Methods
104
vi
CONTENTS
Chapter
4.
Quantum Mechanics
109
4.1.
Specific Heat of Gases
109
4.2.
Fundamentals of Quantum States 111
4.3.
Operators and
Observables
115
4.4.
Amplitude Evolution
117
4.5.
Particle on a Lattice
125
4.6.
Continuous State Space
129
4.7.
Evolution of Expectations and Conservation Laws
134
4.8.
Path Integral Approach to Quantum Mechanics
136
4.9.
Quantum Statistical Mechanics
140
4.10.
A Differential Equation for the Canonical Density Matrix
145
Bibliography
149
Index
151 |
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| author | Bühler, Oliver |
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| callnumber-subject | QC - Physics |
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| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| format | Book |
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| index_date | 2024-07-02T22:02:50Z |
| indexdate | 2024-07-09T21:21:27Z |
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| spelling | Bühler, Oliver Verfasser (DE-588)1073308537 aut A brief introduction to classical, statistical, and quantum mechanics Oliver Bühler New York, NY Courant Inst. of Math. Sciences [u.a.] 2006 VII, 153 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Courant lecture notes in mathematics 13 Includes bibliographical references and index Klassieke mechanica gtt Kwantummechanica gtt Physique mathématique Statistische mechanica gtt Théorie quantique Quantentheorie Quantum theory Mechanics Statistical mechanics Mechanik (DE-588)4038168-7 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf (DE-588)4006432-3 Bibliografie gnd-content Quantentheorie (DE-588)4047992-4 s Mechanik (DE-588)4038168-7 s Statistische Mechanik (DE-588)4056999-8 s DE-604 Erscheint auch als Online-Ausgabe (DE-604)BV043999126 Courant lecture notes in mathematics 13 (DE-604)BV012714106 13 http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2099424&custom_att_2=simple_viewer A brief introduction to classical, statistical, and quantum mechanics Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016735781&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bühler, Oliver A brief introduction to classical, statistical, and quantum mechanics Courant lecture notes in mathematics Klassieke mechanica gtt Kwantummechanica gtt Physique mathématique Statistische mechanica gtt Théorie quantique Quantentheorie Quantum theory Mechanics Statistical mechanics Mechanik (DE-588)4038168-7 gnd Statistische Mechanik (DE-588)4056999-8 gnd Quantentheorie (DE-588)4047992-4 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4056999-8 (DE-588)4047992-4 (DE-588)4006432-3 |
| title | A brief introduction to classical, statistical, and quantum mechanics |
| title_auth | A brief introduction to classical, statistical, and quantum mechanics |
| title_exact_search | A brief introduction to classical, statistical, and quantum mechanics |
| title_exact_search_txtP | A brief introduction to classical, statistical, and quantum mechanics |
| title_full | A brief introduction to classical, statistical, and quantum mechanics Oliver Bühler |
| title_fullStr | A brief introduction to classical, statistical, and quantum mechanics Oliver Bühler |
| title_full_unstemmed | A brief introduction to classical, statistical, and quantum mechanics Oliver Bühler |
| title_short | A brief introduction to classical, statistical, and quantum mechanics |
| title_sort | a brief introduction to classical statistical and quantum mechanics |
| topic | Klassieke mechanica gtt Kwantummechanica gtt Physique mathématique Statistische mechanica gtt Théorie quantique Quantentheorie Quantum theory Mechanics Statistical mechanics Mechanik (DE-588)4038168-7 gnd Statistische Mechanik (DE-588)4056999-8 gnd Quantentheorie (DE-588)4047992-4 gnd |
| topic_facet | Klassieke mechanica Kwantummechanica Physique mathématique Statistische mechanica Théorie quantique Quantentheorie Quantum theory Mechanics Statistical mechanics Mechanik Statistische Mechanik Bibliografie |
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