Quantum Theory of Conducting Matter: Newtonian Equations of Motion for a Bloch Electron
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2007
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 244 S. Ill., graph. Darst. 229 mm x 152 mm |
| ISBN: | 9780387741024 038774102X |
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MARC
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| 100 | 1 | |a Fujita, Shigeji |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantum Theory of Conducting Matter |b Newtonian Equations of Motion for a Bloch Electron |c Shigeji Fujita and Kei Ito |
| 264 | 1 | |a New York, NY |b Springer |c 2007 | |
| 300 | |a XIX, 244 S. |b Ill., graph. Darst. |c 229 mm x 152 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
| _version_ | 1804137740223119360 |
|---|---|
| adam_text | Contents
Preface
v
Constants,
Signs, Symbols, and General Remarks
xiii
I Preliminaries
1
1
Introduction
3
1.1
Crystal Lattices
.......................... 3
1.2
Theoretical Background
..................... 5
1.2.1
Metals and Conduction Electrons
............ 5
1.2.2
Quantum Mechanics
................... 6
1.2.3 Heisenberg
Uncertainty Principle
............ 6
1.2.4
Bosons and
Fermions
................... 7
1.2.5
Fermi and
Bose
Distribution Functions
......... 7
1.2.6
Composite Particles
.................... 7
1.2.7
Quasifree Electron Model
................ 8
1.2.8
Electrons and Holes
................. 8
2
Lattice Vibrations and Heat Capacity
11
2.1
Einstein s Theory of Heat Capacity
............... 11
2.2
Debye s Theory of Heat Capacity
................ 15
3
Free Electrons and Heat Capacity
25
3.1
Free Electrons and the Fermi Energy
.............. 25
3.2
Density of States
......................... 30
3.3
Qualitative Discussions
...................... 36
3.4
Quantitative Calculations
.................... 38
ix
χ
Contents
4 Electric
Conduction
and the Hall Effect
43
4.1
Ohm s Law and Matthiessen s Rule
............... 43
4.2
Motion of a Charged Particle in
Electromagnetic Fields
..................... 46
4.3
The Landau States and Levels
.................. 48
4.4
The Degeneracy of the Landau Levels
.............. 51
4.5
The Hall Effect: Electrons and Holes
............ 56
5
Magnetic Susceptibility
61
5.1
The Magnetogyric Ratio
..................... 61
5.2
Pauli Paramagnetism
....................... 64
5.3
Landau Diamagnetism
...................... 67
6
Boltzmann Equation Method
75
6.1
The Boltzmann Equation
.....................75
6.2
The Current Relaxation Rate
..................78
II Bloch Electron Dynamics
83
7
Bloch Theorem
85
7.1
The Bloch Theorem
........................85
7.2
The Kronig-Penney Model
....................
gì
8
The Fermi Liquid Model
97
8.1
The Self-consistent Field Approximation
............97
8.2
Fermi Liquid Model
........................99
9
The Fermi Surface
103
9.1
Monovalent
Metals
(Na, Cu)
...................103
9.2
Multivalent Metals
........................107
9.3
Electronic Heat Capacity and Density of States
........
Ill
10
Bloch Electron Dynamics
И5
10.1
Introduction
............................
И5
10.2
Newtonian Equations of Motion
.................
yj
10.3
Discussion
.............................123
Contents xi
III
Applications. Fermionic Systems
(Electrons)
131
11 De Haas—
Van Alphen
Oscillations
133
11.1
Onsager s Formula
........................133
11.2
Statistical Mechanical Calculations:
3D.............139
11.3
Statistical Mechanical Calculations: 2D
.............142
11.4
Two-Dimensional Conductors
..................147
12 Magnetoresistance 151
12.1
Introduction
............................151
12.2 Anisotropie Magnetoresistance
in
Cu
..............153
12.3
Shubnikov-De Haas Oscillations
.................155
12.4
Heterojunction GaAs/AlGaAs
..................161
13
Cyclotron Resonance
171
13.1
Introduction
............................171
13.2
Cyclotron Resonance in Ge and Si
................172
13.3
Cyclotron Resonance in
Al
....................184
13.4
Cyclotron Resonance in Pb
....................188
13.5
Cyclotron Resonance in Zn and
Cd
(НСР)
...........192
14
Seebeck Coefficient (Thermopower)
195
14.1
Introduction
............................195
14.2
Quantum Theory
.........................197
14.3
Discussion
.............................200
15
Infrared Hall Effect
205
15.1
Introduction
............................205
15.2
Kinetic Theory
..........................209
15.2.1
Conductivity
.......................209
15.2.2
Hall Coefficient
......................209
15.2.3
Hall Angle
.........................210
15.2.4
Dynamic Coefficients
...................210
15.3
Discussion
.............................213
Appendix A: Electromagnetic Potentials
217
xii Contents
Appendix
В:
Statistical Weight for the Landau States
221
B.I The Three-Dimensional Case
..................221
B.2 The Two-Dimensional Case
...................223
Appendix C: Derivation of Equation
(11.19) 225
References
227
Bibliography
233
Index
237
|
| adam_txt |
Contents
Preface
v
Constants,
Signs, Symbols, and General Remarks
xiii
I Preliminaries
1
1
Introduction
3
1.1
Crystal Lattices
. 3
1.2
Theoretical Background
. 5
1.2.1
Metals and Conduction Electrons
. 5
1.2.2
Quantum Mechanics
. 6
1.2.3 Heisenberg
Uncertainty Principle
. 6
1.2.4
Bosons and
Fermions
. 7
1.2.5
Fermi and
Bose
Distribution Functions
. 7
1.2.6
Composite Particles
. 7
1.2.7
Quasifree Electron Model
. 8
1.2.8
"Electrons" and "Holes"
. 8
2
Lattice Vibrations and Heat Capacity
11
2.1
Einstein's Theory of Heat Capacity
. 11
2.2
Debye's Theory of Heat Capacity
. 15
3
Free Electrons and Heat Capacity
25
3.1
Free Electrons and the Fermi Energy
. 25
3.2
Density of States
. 30
3.3
Qualitative Discussions
. 36
3.4
Quantitative Calculations
. 38
ix
χ
Contents
4 Electric
Conduction
and the Hall Effect
43
4.1
Ohm's Law and Matthiessen's Rule
. 43
4.2
Motion of a Charged Particle in
Electromagnetic Fields
. 46
4.3
The Landau States and Levels
. 48
4.4
The Degeneracy of the Landau Levels
. 51
4.5
The Hall Effect: "Electrons" and "Holes"
. 56
5
Magnetic Susceptibility
61
5.1
The Magnetogyric Ratio
. 61
5.2
Pauli Paramagnetism
. 64
5.3
Landau Diamagnetism
. 67
6
Boltzmann Equation Method
75
6.1
The Boltzmann Equation
.75
6.2
The Current Relaxation Rate
.78
II Bloch Electron Dynamics
83
7
Bloch Theorem
85
7.1
The Bloch Theorem
.85
7.2
The Kronig-Penney Model
.
gì
8
The Fermi Liquid Model
97
8.1
The Self-consistent Field Approximation
.97
8.2
Fermi Liquid Model
.99
9
The Fermi Surface
103
9.1
Monovalent
Metals
(Na, Cu)
.103
9.2
Multivalent Metals
.107
9.3
Electronic Heat Capacity and Density of States
.
Ill
10
Bloch Electron Dynamics
И5
10.1
Introduction
.
И5
10.2
Newtonian Equations of Motion
.
\yj
10.3
Discussion
.123
Contents xi
III
Applications. Fermionic Systems
(Electrons)
131
11 De Haas—
Van Alphen
Oscillations
133
11.1
Onsager's Formula
.133
11.2
Statistical Mechanical Calculations:
3D.139
11.3
Statistical Mechanical Calculations: 2D
.142
11.4
Two-Dimensional Conductors
.147
12 Magnetoresistance 151
12.1
Introduction
.151
12.2 Anisotropie Magnetoresistance
in
Cu
.153
12.3
Shubnikov-De Haas Oscillations
.155
12.4
Heterojunction GaAs/AlGaAs
.161
13
Cyclotron Resonance
171
13.1
Introduction
.171
13.2
Cyclotron Resonance in Ge and Si
.172
13.3
Cyclotron Resonance in
Al
.184
13.4
Cyclotron Resonance in Pb
.188
13.5
Cyclotron Resonance in Zn and
Cd
(НСР)
.192
14
Seebeck Coefficient (Thermopower)
195
14.1
Introduction
.195
14.2
Quantum Theory
.197
14.3
Discussion
.200
15
Infrared Hall Effect
205
15.1
Introduction
.205
15.2
Kinetic Theory
.209
15.2.1
Conductivity
.209
15.2.2
Hall Coefficient
.209
15.2.3
Hall Angle
.210
15.2.4
Dynamic Coefficients
.210
15.3
Discussion
.213
Appendix A: Electromagnetic Potentials
217
xii Contents
Appendix
В:
Statistical Weight for the Landau States
221
B.I The Three-Dimensional Case
.221
B.2 The Two-Dimensional Case
.223
Appendix C: Derivation of Equation
(11.19) 225
References
227
Bibliography
233
Index
237 |
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| id | DE-604.BV023372099 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:13:00Z |
| indexdate | 2024-07-09T21:17:06Z |
| institution | BVB |
| isbn | 9780387741024 038774102X |
| language | English |
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| physical | XIX, 244 S. Ill., graph. Darst. 229 mm x 152 mm |
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| publisher | Springer |
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| spelling | Fujita, Shigeji Verfasser aut Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron Shigeji Fujita and Kei Ito New York, NY Springer 2007 XIX, 244 S. Ill., graph. Darst. 229 mm x 152 mm txt rdacontent n rdamedia nc rdacarrier Mathematik Conduction electrons Mathematics Equations of motion Quantum electrodynamics Fermi-Fläche (DE-588)4154016-5 gnd rswk-swf Leitfähigkeit (DE-588)4120663-0 gnd rswk-swf Bloch-Elektron (DE-588)4531809-8 gnd rswk-swf Leitfähigkeit (DE-588)4120663-0 s Bloch-Elektron (DE-588)4531809-8 s Fermi-Fläche (DE-588)4154016-5 s DE-604 Itō, Kei Verfasser (DE-588)158973666 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016555348&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fujita, Shigeji Itō, Kei Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron Mathematik Conduction electrons Mathematics Equations of motion Quantum electrodynamics Fermi-Fläche (DE-588)4154016-5 gnd Leitfähigkeit (DE-588)4120663-0 gnd Bloch-Elektron (DE-588)4531809-8 gnd |
| subject_GND | (DE-588)4154016-5 (DE-588)4120663-0 (DE-588)4531809-8 |
| title | Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron |
| title_auth | Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron |
| title_exact_search | Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron |
| title_exact_search_txtP | Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron |
| title_full | Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron Shigeji Fujita and Kei Ito |
| title_fullStr | Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron Shigeji Fujita and Kei Ito |
| title_full_unstemmed | Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron Shigeji Fujita and Kei Ito |
| title_short | Quantum Theory of Conducting Matter |
| title_sort | quantum theory of conducting matter newtonian equations of motion for a bloch electron |
| title_sub | Newtonian Equations of Motion for a Bloch Electron |
| topic | Mathematik Conduction electrons Mathematics Equations of motion Quantum electrodynamics Fermi-Fläche (DE-588)4154016-5 gnd Leitfähigkeit (DE-588)4120663-0 gnd Bloch-Elektron (DE-588)4531809-8 gnd |
| topic_facet | Mathematik Conduction electrons Mathematics Equations of motion Quantum electrodynamics Fermi-Fläche Leitfähigkeit Bloch-Elektron |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016555348&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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