Green's functions in quantum physics:
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1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Berlin [u.a.]
Springer
2006
|
Ausgabe: | 3. ed. |
Schriftenreihe: | Springer series in solid-state sciences
7 |
Schlagworte: | |
Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
Beschreibung: | XVII, 477 S. graph. Darst. 235 mm x 155 mm |
ISBN: | 3540288384 9783540288381 |
Internformat
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100 | 1 | |a Economou, Eleftherios N. |d 1940- |e Verfasser |0 (DE-588)10952473X |4 aut | |
245 | 1 | 0 | |a Green's functions in quantum physics |c Eleftherios N. Economou |
250 | |a 3. ed. | ||
264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
300 | |a XVII, 477 S. |b graph. Darst. |c 235 mm x 155 mm | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Springer series in solid-state sciences |v 7 | |
650 | 4 | |a Quantentheorie | |
650 | 4 | |a Green's functions | |
650 | 4 | |a Quantum theory | |
650 | 0 | 7 | |a Quantenphysik |0 (DE-588)4266670-3 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
_version_ | 1805083323912945664 |
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adam_text |
Contents
Part I Green's Functions in Mathematical Physics
1
Time-Independent Green's Functions
. 3
1.1
Formalism
. 3
1.2
Examples
. 9
1.2.1
Three-Dimensional Case (d
= 3). 10
1.2.2
Two-Dimensional Case (d
= 2). 11
1.2.3
One-Dimensional Case (d
= 1). 13
1.2.4
Finite Domain
Ω
. 13
1.3
Summary
. 14
1.3.1
Definition
. 14
1.3.2
Basic Properties
. 15
1.3.3
Methods of Calculation
. 15
1.3.4
Use
. 16
Further Reading
. 17
Problems
. 17
2
Time-Dependent Green's Functions
. 21
2.1
First-Order Case
. 21
2.1.1
Examples
. 24
2.2
Second-Order Case
. 26
2.2.1
Examples
. 30
2.3
Summary
. 33
2.3.1
Definition
. 33
2.3.2
Basic Properties
. 33
2.3.3
Definition
. 34
2.3.4
Basic Properties
. 34
2.3.5
Use
. 35
Further Reading
. 36
Problems
. 36
XIV Contents
Part II Green's Functions in One-Body Quantum Problems
3
Physical Significance of G.
Application to the Free-Particle Case
. 41
3.1
General Relations
. 41
3.2
The Free-Particle
(По
=
ρ2
/2m) Case
. 43
3.2.1
3-d Case
. 44
3.2.2
2-d Case
. 45
3.2.3
1-d Case
. 45
3.3
The Free-Particle Klein-Gordon Case
. 47
3.4
Summary
. 50
Further Reading
. 51
Problems
. 51
4
Green's Functions and Perturbation Theory
. 55
4.1
Formalism
. 55
4.1.1
Time-Independent Case
. 55
4.1.2
Time-Dependent Case
. 60
4.2
Applications
. 64
4.2.1
Scattering Theory (E
> 0). 64
4.2.2
Bound State in Shallow Potential Wells (E
< 0). 67
4.2.3
The KKR Method for Electronic Calculations in Solids
. 70
4.3
Summary
. 71
Further Reading
. 74
Problems
. 74
5
Green's Functions for Tight-Binding Hamiltonians
. 77
5.1
Introductory Remarks
. 77
5.2
The Tight-Binding Hamiltonian (TBH)
. 80
5.3
Green's Functions
. 87
5.3.1
One-Dimensional Lattice
. 88
5.3.2
Square Lattice
. 89
5.3.3
Simple Cubic Lattice
. 94
5.3.4
Green's Functions for Bethe Lattices (Cayley Trees)
. 98
5.4
Summary
.101
Further Reading
.102
Problems
.102
6
Single Impurity Scattering
.
\\\
6.1
Formalism
.
щ
6.2
Explicit Results for a Single Band
.118
6.2.1
Three-Dimensional Case
.118
6.2.2
Two-Dimensional Case
.123
6.2.3
One-Dimensional Case
.124
Contents
XV
6.3 Applications.125
6.3.1
Levels in the Gap
.125
6.3.2
The Cooper Pair and Superconductivity
.127
6.3.3
The Kondo Problem
.133
6.3.4
Lattice Vibrations in Crystals Containing "Isotope"
Impurities
.135
6.4
Summary
.137
Further Reading
.139
Problems
.140
Two or More Impurities; Disordered Systems
.141
7.1
Two Impurities
.141
7.2
Infinite Number of Impurities
.150
7.2.1
Virtual Crystal Approximation (VCA)
.151
7.2.2
Average ¿-Matrix Approximation (ATA)
.152
7.2.3
Coherent Potential Approximation
(СРА)
.153
7.2.4
The
СРА
for Classical Waves
.158
7.2.5
Direct Extensions of the
СРА
.163
7.2.6
Cluster Generalizations of the
СРА
.165
7.3
Summary
.168
Further Reading
.169
Problems
.169
Electrical Conductivity and Green's Functions
.173
8.1
Electrical Conductivity and Related Quantities
.173
8.2
Various Methods of Calculation
.176
8.2.1
Phenomenological Approach
.176
8.2.2
Boltzmann's Equation
.177
8.2.3
A General, Independent-Particle Formula
for Conductivity
.178
8.2.4
General Linear Response Theory
.180
8.3
Conductivity in Terms of Green's Functions
.183
8.3.1
Conductivity Without Vertex Corrections
.184
8.3.2
СРА
for Vertex Corrections
.
І86
8.3.3
Vertex Corrections Beyond the
СРА
.190
8.3.4
Post-CPA Corrections to Conductivity
.192
8.4
Summary
.195
Further Reading
.197
Problems
.197
Localization, Transport, and Green's Functions
.199
9.1
An Overview
.199
9.2
Disorder, Diffusion, and Interference
.203
9.3
Localization
.208
9.3.1
Three-Dimensional Systems
.210
XVI Contents
9.3.2
Two-Dimensional Systems
.212
9.3.3
One-Dimensional and Quasi-One-Dimensional Systems
. 214
9.4
Conductance and Transmission
.216
9.5
Scaling Approach
.219
9.6
Other Calculational Techniques
.224
9.6.1
Quasi-One-Dimensional Systems and Scaling
.225
9.6.2
Level Spacing Statistics
.225
9.7
Localization and Green's Functions
.226
9.7.1
Green's Function and Localization in One Dimension
. 227
9.7.2
Renormalized Perturbation Expansion (RPE)
and Localization
.230
9.7.3
Green's Functions and Transmissions
in Quasi-One-Dimensional Systems
.235
9.8
Applications
.238
9.9
Summary
.240
Further Reading
.243
Problems
.243
Part III Green's Functions in Many-Body Systems
10
Definitions
.249
10.1
Single-Particle Green's Functions in Terms of Field Operators
. 249
10.2
Green's Functions for Interacting Particles
.253
10.3
Green's Functions for Noninteracting Particles
.257
10.4
Summary
.260
Further Reading
.261
Problems
.261
11
Properties and Use of the Green's Functions
.263
11.1
Analytical Properties of gs and gs
.263
11.2
Physical Significance and Use of gs and 7j&
.268
11.3
Quasiparticles
.275
11.4
Summary
.281
11.4.1
Properties
.281
11.4.2
Use
.282
Further Reading
.283
Problems
.283
12
Calculational Methods for
g
.285
12.1
Equation of Motion Method
.285
12.2
Diagrammatic Method for
Fermions
at
Τ
- 0.289
12.3
Diagrammatic Method for
Τ φ
0.298
12.4
Partial Summations. Dyson's Equation
.300
12.5
Other Methods of Calculation
.306
Contents XVII
12.6
Summary
.306
Further Reading
.307
Problems
.307
13
Applications
.309
13.1
Normal Fermi Systems. Landau Theory
.309
13.2
High-Density Electron Gas
.312
13.3
Dilute Fermi Gas
.319
13.4
Superconductivity
.322
13.4.1
Diagrammatic Approach
.322
13.4.2
Equation of Motion Approach
.324
13.5
The Hubbard Model
.327
13.6
Summary
.332
Further Reading
.333
Problems
.334
A Dirac's delta Function
.337
В
Dirac's bra and
ket
Notation
.341
С
Solutions of Laplace and Helmholtz Equations
in Various Coordinate Systems
.345
C.I Helmholtz Equation (V2
+
k2)
φ
(r) =
0.345
C.I.I Cartesian Coordinates
x, y, z
.345
С.
1.2
Cylindrical Coordinates
ζ, φ,
Q.
345
С.
1.3
Spherical coordinates
r,
θ, φ.
346
C.2
Vector Derivatives
.347
C.2.1 Spherical Coordinates r,
θ, φ
.347
C.2.
2
Cylindrical Coordinates
ζ, ρ, φ.
348
С.З
Schrödinger
Equation in Centrally
Symmetrie
3-
and 2-Dimensional
Potential
V
.348
D
Analytic Behavior of
G (z)
Near a Band Edge
.351
E
Wannier Functions
.355
F
Renormalized Perturbation Expansion (RPE)
.357
G Boltzmann's
Equation
.363
H
Transfer Matrix, S-Matrix, etc
.369
I Second Quantization
.379
Solutions of Selected Problems
.391
References
.447
Index
.461 |
adam_txt |
Contents
Part I Green's Functions in Mathematical Physics
1
Time-Independent Green's Functions
. 3
1.1
Formalism
. 3
1.2
Examples
. 9
1.2.1
Three-Dimensional Case (d
= 3). 10
1.2.2
Two-Dimensional Case (d
= 2). 11
1.2.3
One-Dimensional Case (d
= 1). 13
1.2.4
Finite Domain
Ω
. 13
1.3
Summary
. 14
1.3.1
Definition
. 14
1.3.2
Basic Properties
. 15
1.3.3
Methods of Calculation
. 15
1.3.4
Use
. 16
Further Reading
. 17
Problems
. 17
2
Time-Dependent Green's Functions
. 21
2.1
First-Order Case
. 21
2.1.1
Examples
. 24
2.2
Second-Order Case
. 26
2.2.1
Examples
. 30
2.3
Summary
. 33
2.3.1
Definition
. 33
2.3.2
Basic Properties
. 33
2.3.3
Definition
. 34
2.3.4
Basic Properties
. 34
2.3.5
Use
. 35
Further Reading
. 36
Problems
. 36
XIV Contents
Part II Green's Functions in One-Body Quantum Problems
3
Physical Significance of G.
Application to the Free-Particle Case
. 41
3.1
General Relations
. 41
3.2
The Free-Particle
(По
=
ρ2
/2m) Case
. 43
3.2.1
3-d Case
. 44
3.2.2
2-d Case
. 45
3.2.3
1-d Case
. 45
3.3
The Free-Particle Klein-Gordon Case
. 47
3.4
Summary
. 50
Further Reading
. 51
Problems
. 51
4
Green's Functions and Perturbation Theory
. 55
4.1
Formalism
. 55
4.1.1
Time-Independent Case
. 55
4.1.2
Time-Dependent Case
. 60
4.2
Applications
. 64
4.2.1
Scattering Theory (E
> 0). 64
4.2.2
Bound State in Shallow Potential Wells (E
< 0). 67
4.2.3
The KKR Method for Electronic Calculations in Solids
. 70
4.3
Summary
. 71
Further Reading
. 74
Problems
. 74
5
Green's Functions for Tight-Binding Hamiltonians
. 77
5.1
Introductory Remarks
. 77
5.2
The Tight-Binding Hamiltonian (TBH)
. 80
5.3
Green's Functions
. 87
5.3.1
One-Dimensional Lattice
. 88
5.3.2
Square Lattice
. 89
5.3.3
Simple Cubic Lattice
. 94
5.3.4
Green's Functions for Bethe Lattices (Cayley Trees)
. 98
5.4
Summary
.101
Further Reading
.102
Problems
.102
6
Single Impurity Scattering
.
\\\
6.1
Formalism
.
щ
6.2
Explicit Results for a Single Band
.118
6.2.1
Three-Dimensional Case
.118
6.2.2
Two-Dimensional Case
.123
6.2.3
One-Dimensional Case
.124
Contents
XV
6.3 Applications.125
6.3.1
Levels in the Gap
.125
6.3.2
The Cooper Pair and Superconductivity
.127
6.3.3
The Kondo Problem
.133
6.3.4
Lattice Vibrations in Crystals Containing "Isotope"
Impurities
.135
6.4
Summary
.137
Further Reading
.139
Problems
.140
Two or More Impurities; Disordered Systems
.141
7.1
Two Impurities
.141
7.2
Infinite Number of Impurities
.150
7.2.1
Virtual Crystal Approximation (VCA)
.151
7.2.2
Average ¿-Matrix Approximation (ATA)
.152
7.2.3
Coherent Potential Approximation
(СРА)
.153
7.2.4
The
СРА
for Classical Waves
.158
7.2.5
Direct Extensions of the
СРА
.163
7.2.6
Cluster Generalizations of the
СРА
.165
7.3
Summary
.168
Further Reading
.169
Problems
.169
Electrical Conductivity and Green's Functions
.173
8.1
Electrical Conductivity and Related Quantities
.173
8.2
Various Methods of Calculation
.176
8.2.1
Phenomenological Approach
.176
8.2.2
Boltzmann's Equation
.177
8.2.3
A General, Independent-Particle Formula
for Conductivity
.178
8.2.4
General Linear Response Theory
.180
8.3
Conductivity in Terms of Green's Functions
.183
8.3.1
Conductivity Without Vertex Corrections
.184
8.3.2
СРА
for Vertex Corrections
.
І86
8.3.3
Vertex Corrections Beyond the
СРА
.190
8.3.4
Post-CPA Corrections to Conductivity
.192
8.4
Summary
.195
Further Reading
.197
Problems
.197
Localization, Transport, and Green's Functions
.199
9.1
An Overview
.199
9.2
Disorder, Diffusion, and Interference
.203
9.3
Localization
.208
9.3.1
Three-Dimensional Systems
.210
XVI Contents
9.3.2
Two-Dimensional Systems
.212
9.3.3
One-Dimensional and Quasi-One-Dimensional Systems
. 214
9.4
Conductance and Transmission
.216
9.5
Scaling Approach
.219
9.6
Other Calculational Techniques
.224
9.6.1
Quasi-One-Dimensional Systems and Scaling
.225
9.6.2
Level Spacing Statistics
.225
9.7
Localization and Green's Functions
.226
9.7.1
Green's Function and Localization in One Dimension
. 227
9.7.2
Renormalized Perturbation Expansion (RPE)
and Localization
.230
9.7.3
Green's Functions and Transmissions
in Quasi-One-Dimensional Systems
.235
9.8
Applications
.238
9.9
Summary
.240
Further Reading
.243
Problems
.243
Part III Green's Functions in Many-Body Systems
10
Definitions
.249
10.1
Single-Particle Green's Functions in Terms of Field Operators
. 249
10.2
Green's Functions for Interacting Particles
.253
10.3
Green's Functions for Noninteracting Particles
.257
10.4
Summary
.260
Further Reading
.261
Problems
.261
11
Properties and Use of the Green's Functions
.263
11.1
Analytical Properties of gs and gs
.263
11.2
Physical Significance and Use of gs and 7j&
.268
11.3
Quasiparticles
.275
11.4
Summary
.281
11.4.1
Properties
.281
11.4.2
Use
.282
Further Reading
.283
Problems
.283
12
Calculational Methods for
g
.285
12.1
Equation of Motion Method
.285
12.2
Diagrammatic Method for
Fermions
at
Τ
- 0.289
12.3
Diagrammatic Method for
Τ φ
0.298
12.4
Partial Summations. Dyson's Equation
.300
12.5
Other Methods of Calculation
.306
Contents XVII
12.6
Summary
.306
Further Reading
.307
Problems
.307
13
Applications
.309
13.1
Normal Fermi Systems. Landau Theory
.309
13.2
High-Density Electron Gas
.312
13.3
Dilute Fermi Gas
.319
13.4
Superconductivity
.322
13.4.1
Diagrammatic Approach
.322
13.4.2
Equation of Motion Approach
.324
13.5
The Hubbard Model
.327
13.6
Summary
.332
Further Reading
.333
Problems
.334
A Dirac's delta Function
.337
В
Dirac's bra and
ket
Notation
.341
С
Solutions of Laplace and Helmholtz Equations
in Various Coordinate Systems
.345
C.I Helmholtz Equation (V2
+
k2)
φ
(r) =
0.345
C.I.I Cartesian Coordinates
x, y, z
.345
С.
1.2
Cylindrical Coordinates
ζ, φ,
Q.
345
С.
1.3
Spherical coordinates
r,
θ, φ.
346
C.2
Vector Derivatives
.347
C.2.1 Spherical Coordinates r,
θ, φ
.347
C.2.
2
Cylindrical Coordinates
ζ, ρ, φ.
348
С.З
Schrödinger
Equation in Centrally
Symmetrie
3-
and 2-Dimensional
Potential
V
.348
D
Analytic Behavior of
G (z)
Near a Band Edge
.351
E
Wannier Functions
.355
F
Renormalized Perturbation Expansion (RPE)
.357
G Boltzmann's
Equation
.363
H
Transfer Matrix, S-Matrix, etc
.369
I Second Quantization
.379
Solutions of Selected Problems
.391
References
.447
Index
.461 |
any_adam_object | 1 |
any_adam_object_boolean | 1 |
author | Economou, Eleftherios N. 1940- |
author_GND | (DE-588)10952473X |
author_facet | Economou, Eleftherios N. 1940- |
author_role | aut |
author_sort | Economou, Eleftherios N. 1940- |
author_variant | e n e en ene |
building | Verbundindex |
bvnumber | BV021681979 |
callnumber-first | Q - Science |
callnumber-label | QC174 |
callnumber-raw | QC174.17.G68 |
callnumber-search | QC174.17.G68 |
callnumber-sort | QC 3174.17 G68 |
callnumber-subject | QC - Physics |
classification_rvk | UK 1200 UP 1100 LE 1851 |
classification_tum | PHY 022f PHY 013f |
ctrlnum | (OCoLC)70573702 (DE-599)BVBBV021681979 |
dewey-full | 530.12 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 530 - Physics |
dewey-raw | 530.12 |
dewey-search | 530.12 |
dewey-sort | 3530.12 |
dewey-tens | 530 - Physics |
discipline | Physik Klassische Archäologie |
discipline_str_mv | Physik |
edition | 3. ed. |
format | Book |
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id | DE-604.BV021681979 |
illustrated | Illustrated |
index_date | 2024-07-02T15:11:40Z |
indexdate | 2024-07-20T07:46:43Z |
institution | BVB |
isbn | 3540288384 9783540288381 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014896180 |
oclc_num | 70573702 |
open_access_boolean | |
owner | DE-29T DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-83 DE-11 DE-384 |
owner_facet | DE-29T DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-83 DE-11 DE-384 |
physical | XVII, 477 S. graph. Darst. 235 mm x 155 mm |
publishDate | 2006 |
publishDateSearch | 2006 |
publishDateSort | 2006 |
publisher | Springer |
record_format | marc |
series | Springer series in solid-state sciences |
series2 | Springer series in solid-state sciences |
spelling | Economou, Eleftherios N. 1940- Verfasser (DE-588)10952473X aut Green's functions in quantum physics Eleftherios N. Economou 3. ed. Berlin [u.a.] Springer 2006 XVII, 477 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer series in solid-state sciences 7 Quantentheorie Green's functions Quantum theory Quantenphysik (DE-588)4266670-3 gnd rswk-swf Green-Funktion (DE-588)4158123-4 gnd rswk-swf Mehrpunktfunktion (DE-588)4371838-3 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Green-Funktion (DE-588)4158123-4 s Quantenmechanik (DE-588)4047989-4 s DE-604 Quantentheorie (DE-588)4047992-4 s 1\p DE-604 Mehrpunktfunktion (DE-588)4371838-3 s 2\p DE-604 Quantenphysik (DE-588)4266670-3 s 3\p DE-604 Springer series in solid-state sciences 7 (DE-604)BV000016582 7 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2671406&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014896180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Economou, Eleftherios N. 1940- Green's functions in quantum physics Springer series in solid-state sciences Quantentheorie Green's functions Quantum theory Quantenphysik (DE-588)4266670-3 gnd Green-Funktion (DE-588)4158123-4 gnd Mehrpunktfunktion (DE-588)4371838-3 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
subject_GND | (DE-588)4266670-3 (DE-588)4158123-4 (DE-588)4371838-3 (DE-588)4047992-4 (DE-588)4047989-4 |
title | Green's functions in quantum physics |
title_auth | Green's functions in quantum physics |
title_exact_search | Green's functions in quantum physics |
title_exact_search_txtP | Green's functions in quantum physics |
title_full | Green's functions in quantum physics Eleftherios N. Economou |
title_fullStr | Green's functions in quantum physics Eleftherios N. Economou |
title_full_unstemmed | Green's functions in quantum physics Eleftherios N. Economou |
title_short | Green's functions in quantum physics |
title_sort | green s functions in quantum physics |
topic | Quantentheorie Green's functions Quantum theory Quantenphysik (DE-588)4266670-3 gnd Green-Funktion (DE-588)4158123-4 gnd Mehrpunktfunktion (DE-588)4371838-3 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
topic_facet | Quantentheorie Green's functions Quantum theory Quantenphysik Green-Funktion Mehrpunktfunktion Quantenmechanik |
url | http://deposit.dnb.de/cgi-bin/dokserv?id=2671406&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014896180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000016582 |
work_keys_str_mv | AT economoueleftheriosn greensfunctionsinquantumphysics |