Path integrals in quantum mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2006
|
| Ausgabe: | reprint.(with corr.) |
| Schriftenreihe: | Oxford graduate texts
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 318 S. graph. Darst. |
| ISBN: | 0198566743 9780198566748 |
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| 245 | 1 | 0 | |a Path integrals in quantum mechanics |c J. Zinn-Justin |
| 250 | |a reprint.(with corr.) | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2006 | |
| 300 | |a XIII, 318 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016768288 | ||
Datensatz im Suchindex
| _version_ | 1804138062246051840 |
|---|---|
| adam_text | Contents
1
Gaussian integrals
.........................1
1.1
Generating function
...................... 1
1.2
Gaussian expectation values. Wick s theorem
........... 2
1.3
Perturbed
gaussian
measure. Connected contributions
....... 6
1.4
Expectation values. Generating function.
Cumulants
........ 9
1.5
Steepest descent method
.................... 12
1.6
Steepest descent method: Several variables, generating functions
... 18
1.7
Gaussian integrals: Complex matrices
............... 20
Exercises
............................. 23
2
Path integrals in quantum mechanics
................ 27
2.1
Local markovian processes
....................28
2.2
Solution of the evolution equation for short times
..........31
2.3
Path integral representation
...................34
2.4
Explicit calculation:
gaussian
path, integrals
............38
2.5
Correlation functions: generating functional
............41
2.6
General
gaussian
path integral and correlation functions
.......44
2.7
Harmonic oscillator: the partition function
............48
2.8
Perturbed harmonic oscillator
..................52
2.9
Perturbative expansion in powers of
ћ
...............54
2.10
Semi-classical expansion
....................55
Exercises
.............................59
3
Partition function and spectrum
..................63
3.1
Perturbative calculation
.....................63
3.2
Semi-classical or WKB expansion
.................66
3.3
Path integral and variatkmal principle
..............73
3.4
O(N) symmetric quartic potential for
N —>■
oo
...........75
3.5
Operator determinants
.....................84
3.6
Hamiltonian: structure of the ground state
............85
Exercises
.............................87
4
Classical and quantum statistical physics
..............91
4.1
Classical partition function. Transfer matrix
............91
4.2
Correlation functions
......................94
xii Contents
4.3
Classical model at low temperature: an example
..........97
4.4
Continuum limit and path integral
................98
4.5
The two-point function: perturbative expansion, spectral representation
102
4.6
Operator formalism. Time-ordered products
........... 105
Exercises
............................ 107
5
Path integrals and quantization
..................
Ill
5.1
Gauge transformations
....................
Ill
5.2
Coupling to a magnetic field: gauge symmetry
.......... 113
5.3
Quantization and path integrals
................ 116
5.4
Magnetic field: direct calculation
................ 120
5.5
Diffusion, random walk, Fokker-Planck equation
......... 122
5.6
The spectrum of the O(2) rigid rotator
............. 126
Exercises
............................ 131
6
Path integrals and holomorphic formalism
............. 135
6.1
Complex integrals and Wick s theorem
............. 135
6.2
Holomorphic representation
.................. 140
6.3
Kernel of operators
...................... 143
6.4
Path integral: the harmonic oscillator
.............. 146
6.5
Path integral: general hamiltonians
............... 150
6.6
Bosons: second quantization
.................. 156
6.7
Partition function
...................... 159
6.8
Bose-Einstein condensation
.................. 161
6.9
Generalized path integrals: the quantum
Bose
gas
........ 164
Exercises
............................ 169
7
Path integrals:
fermions
..................... 179
7.1 Grassmann
algebras
..................... 179
7.2
Differentiation in
Grassmann
algebras
.............. 181
7.3
Integration in
Grassmann
algebras
............... 182
7.4
Gaussian integrals and perturbative expansion
.......... 184
7.5
Fermion vector space and operators
............... 190
7.6
One-state hamiltonian
.................... 195
7.7
Many-particle states. Partition function
............. 197
7.8
Path integral: one-state problem
................ 200
7.9
Path integrals: Generalization
................. 203
7.10
Quantum Fermi gas
..................... 206
7.11
Real
gaussian
integrals. Wick s theorem
............ 210
7.12
Mixed change of variables: Berezinian and
supertrace
...... 212
Exercises
............................ 214
8
Barrier penetration: semi-classical approximation
.......... 225
8.1
Quartic double-well potential and
instantons
........... 225
8.2
Degenerate minima: semi-classical approximation
......... 229
8.3
Collective coordinates and
gaussian
integration
.......... 232
8.4
Instantons
and metastable states
................ 238
8.5
Collective coordinates: alternative method
............ 243
8.6
The jacobian
......................... 245
Contents xiii
8.7 Instantons:
the quartic anharmonic oscillator
.......... 247
Exercises
............................ 251
9
Quantum evolution and scattering matrix
............. 257
9.1
Evolution of the free particle and ^-matrix
........... 257
9.2
Perturbative expansion of the
¿v-matrix ............. 260
9.3
^-matrix: bosons and
fermions
................. 266
9.4
S-mátrix
in the semi-classical limit
............... 269
9.5
Semi-classical approximation: one dimension
........... 270
9.6
Eikonal approximation
.................... 272
9.7
Perturbation theory and operators
............... 276
Exercises
............................ 277
10
Path integrals in phase space
.................. 279
10.1
A few elements of classical mechanics
............. 279
10.2
The path integral in phase space
............... 284
10.3
Harmonic oscillator. Perturbative calculations
.......... 289
10.4
Lagrangians quadratic in the velocities
............. 290
10.5
Free motion on the sphere or rigid rotator
........... 294
Exercises
............................ 299
Appendix Quantum mechanics: minimal background
........ 301
Al
Hubert space and operators
.................. 301
A2 Quantum evolution, symmetries and density matrix
........ 303
A3
Position and momentum.
Schrödinger
equation
.......... 305
Bibliography
........................... 311
Index
............................... 315
|
| adam_txt |
Contents
1
Gaussian integrals
.1
1.1
Generating function
. 1
1.2
Gaussian expectation values. Wick's theorem
. 2
1.3
Perturbed
gaussian
measure. Connected contributions
. 6
1.4
Expectation values. Generating function.
Cumulants
. 9
1.5
Steepest descent method
. 12
1.6
Steepest descent method: Several variables, generating functions
. 18
1.7
Gaussian integrals: Complex matrices
. 20
Exercises
. 23
2
Path integrals in quantum mechanics
. 27
2.1
Local markovian processes
.28
2.2
Solution of the evolution equation for short times
.31
2.3
Path integral representation
.34
2.4
Explicit calculation:
gaussian
path, integrals
.38
2.5
Correlation functions: generating functional
.41
2.6
General
gaussian
path integral and correlation functions
.44
2.7
Harmonic oscillator: the partition function
.48
2.8
Perturbed harmonic oscillator
.52
2.9
Perturbative expansion in powers of
ћ
.54
2.10
Semi-classical expansion
.55
Exercises
.59
3
Partition function and spectrum
.63
3.1
Perturbative calculation
.63
3.2
Semi-classical or WKB expansion
.66
3.3
Path integral and variatkmal principle
.73
3.4
O(N) symmetric quartic potential for
N —>■
oo
.75
3.5
Operator determinants
.84
3.6
Hamiltonian: structure of the ground state
.85
Exercises
.87
4
Classical and quantum statistical physics
.91
4.1
Classical partition function. Transfer matrix
.91
4.2
Correlation functions
.94
xii Contents
4.3
Classical model at low temperature: an example
.97
4.4
Continuum limit and path integral
.98
4.5
The two-point function: perturbative expansion, spectral representation
102
4.6
Operator formalism. Time-ordered products
. 105
Exercises
. 107
5
Path integrals and quantization
.
Ill
5.1
Gauge transformations
.
Ill
5.2
Coupling to a magnetic field: gauge symmetry
. 113
5.3
Quantization and path integrals
. 116
5.4
Magnetic field: direct calculation
. 120
5.5
Diffusion, random walk, Fokker-Planck equation
. 122
5.6
The spectrum of the O(2) rigid rotator
. 126
Exercises
. 131
6
Path integrals and holomorphic formalism
. 135
6.1
Complex integrals and Wick's theorem
. 135
6.2
Holomorphic representation
. 140
6.3
Kernel of operators
. 143
6.4
Path integral: the harmonic oscillator
. 146
6.5
Path integral: general hamiltonians
. 150
6.6
Bosons: second quantization
. 156
6.7
Partition function
. 159
6.8
Bose-Einstein condensation
. 161
6.9
Generalized path integrals: the quantum
Bose
gas
. 164
Exercises
. 169
7
Path integrals:
fermions
. 179
7.1 Grassmann
algebras
. 179
7.2
Differentiation in
Grassmann
algebras
. 181
7.3
Integration in
Grassmann
algebras
. 182
7.4
Gaussian integrals and perturbative expansion
. 184
7.5
Fermion vector space and operators
. 190
7.6
One-state hamiltonian
. 195
7.7
Many-particle states. Partition function
. 197
7.8
Path integral: one-state problem
. 200
7.9
Path integrals: Generalization
. 203
7.10
Quantum Fermi gas
. 206
7.11
Real
gaussian
integrals. Wick's theorem
. 210
7.12
Mixed change of variables: Berezinian and
supertrace
. 212
Exercises
. 214
8
Barrier penetration: semi-classical approximation
. 225
8.1
Quartic double-well potential and
instantons
. 225
8.2
Degenerate minima: semi-classical approximation
. 229
8.3
Collective coordinates and
gaussian
integration
. 232
8.4
Instantons
and metastable states
. 238
8.5
Collective coordinates: alternative method
. 243
8.6
The jacobian
. 245
Contents xiii
8.7 Instantons:
the quartic anharmonic oscillator
. 247
Exercises
. 251
9
Quantum evolution and scattering matrix
. 257
9.1
Evolution of the free particle and ^-matrix
. 257
9.2
Perturbative expansion of the
¿v-matrix . 260
9.3
^-matrix: bosons and
fermions
. 266
9.4
S-mátrix
in the semi-classical limit
. 269
9.5
Semi-classical approximation: one dimension
. 270
9.6
Eikonal approximation
. 272
9.7
Perturbation theory and operators
. 276
Exercises
. 277
10
Path integrals in phase space
. 279
10.1
A few elements of classical mechanics
. 279
10.2
The path integral in phase space
. 284
10.3
Harmonic oscillator. Perturbative calculations
. 289
10.4
Lagrangians quadratic in the velocities
. 290
10.5
Free motion on the sphere or rigid rotator
. 294
Exercises
. 299
Appendix Quantum mechanics: minimal background
. 301
Al
Hubert space and operators
. 301
A2 Quantum evolution, symmetries and density matrix
. 303
A3
Position and momentum.
Schrödinger
equation
. 305
Bibliography
. 311
Index
. 315 |
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| id | DE-604.BV035100306 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:13:59Z |
| indexdate | 2024-07-09T21:22:13Z |
| institution | BVB |
| isbn | 0198566743 9780198566748 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016768288 |
| oclc_num | 315681821 |
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| physical | XIII, 318 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford graduate texts |
| spelling | Zinn-Justin, Jean Verfasser aut Path integrals in quantum mechanics J. Zinn-Justin reprint.(with corr.) Oxford [u.a.] Oxford Univ. Press 2006 XIII, 318 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Pfadintegral (DE-588)4173973-5 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Pfadintegral (DE-588)4173973-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016768288&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zinn-Justin, Jean Path integrals in quantum mechanics Quantenmechanik (DE-588)4047989-4 gnd Pfadintegral (DE-588)4173973-5 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4173973-5 |
| title | Path integrals in quantum mechanics |
| title_auth | Path integrals in quantum mechanics |
| title_exact_search | Path integrals in quantum mechanics |
| title_exact_search_txtP | Path integrals in quantum mechanics |
| title_full | Path integrals in quantum mechanics J. Zinn-Justin |
| title_fullStr | Path integrals in quantum mechanics J. Zinn-Justin |
| title_full_unstemmed | Path integrals in quantum mechanics J. Zinn-Justin |
| title_short | Path integrals in quantum mechanics |
| title_sort | path integrals in quantum mechanics |
| topic | Quantenmechanik (DE-588)4047989-4 gnd Pfadintegral (DE-588)4173973-5 gnd |
| topic_facet | Quantenmechanik Pfadintegral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016768288&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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