Solid state physics: problems and solutions
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Weinheim
Wiley
2004
|
| Schriftenreihe: | Physics textbook
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 261 S. Ill., graph. Darst. - Ill., graph. Darst. |
| ISBN: | 9780471152873 0471152870 |
Internformat
MARC
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| 100 | 1 | |a Mihály, László |d 1949- |e Verfasser |0 (DE-588)13669411X |4 aut | |
| 245 | 1 | 0 | |a Solid state physics |b problems and solutions |c László Mihály ; Michael C. Martin |
| 264 | 1 | |a Weinheim |b Wiley |c 2004 | |
| 300 | |a XIV, 261 S. |b Ill., graph. Darst. - Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Physics textbook | |
| 650 | 0 | 7 | |a Festkörperphysik |0 (DE-588)4016921-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143389-0 |a Aufgabensammlung |2 gnd-content | |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Martin, Michael C. |e Verfasser |0 (DE-588)137007213 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016427323 | ||
Datensatz im Suchindex
| _version_ | 1804137539795156992 |
|---|---|
| adam_text | Contents
Preface
xiii
PART I PROBLEMS
1
Crystal Structures
3
1.1
Problem: Symmetries
9
1.2
Problem: Rotations
9
1.3
Problem: Copper Oxide Layers
10
1.4
Problem: Graphite
11
1.5
Problem: Structure of AxC60
11
1.6
Problem: hep and fee Structures
11
1.7
Problem: hep and bee Structures
11
1.8
Problem: Structure Factor of
АлС60
11
1.9
Problem: Neutron Diffraction Device
12
1.10
Problem: Linear Array of Emitters, Finite Size Effects
12
1.11
Problem: Linear Array of Emitters,
Superlattice 12
1.12
Problem: Powder Diffraction of hep and./cc Crystals
13
1.13
Problem: Momentum Resolution
13
1.14
Problem: Finite Size Effects
13
1.15
Problem: Random Displacement
13
1.16
Problem: Vacancies
14
1.17
Problem: Integrated Scattering Intensity
14
2
Interatomic Forces, Lattice Vibrations
15
2.1
Problem: Madelung Constant
19
2.2
Problem: NaCl Bulk Modulus
19
2.3
Problem: Madelung with Screened Potential
19
2.4
Problem: Triple-axis Spectrometer
20
2.5
Problem: Phonons in Silicon
20
2.6
Problem: Linear Array of Emitters, Phonons
20
2.7
Problem: Long Range Interaction
21
2.8
Problem: Mass Defect
21
2.9
Problem: Debye Frequency
21
2.10
Problem:
Vibrationsofa
Square Lattice
22
vi
Contents
2.11 Problem: Grüneisen Parameter 22
2.12 Problem:
Diatomic
Chain 22
2.13 Problem:
Damped Oscillation
22
2.14 Problem:
Two-Dimensional Debye
23
2.15 Problem:
Soft Optical Phonons
23
2.16
Problem: Soft Phonons Again
23
3
Electronic Band Structure
25
3.1
Problem: Nearly Free Electrons in One Dimension
30
3.2
Problem: Nearly Free Electrons in Dirac-Delta Potentials
30
3.3
Problem: Tight-Binding in Dirac-Delta Potentials
30
3.4
Problem: Dirac-Delta Potentials
31
3.5
Problem: Band Overlap
31
3.6
Problem: Nearly Free Electrons in Two Dimensions
31
3.7
Problem: Nearly Free Electron Bands
32
3.8
Problem: Instability at the Fermi Wavenumber
32
3.9
Problem: Electrons in 2D Nearly Free Electron Band
32
3.10
Problem: Square Lattice
32
3.11
Problem: Tight-Binding Band in Two Dimensions
33
3.12
Problem: Electrons in 2D Tight-Binding Band
33
3.13
Problem: Dirac-Delta Potentials in Two Dimensions
33
3.14
Problem: Effective Mass
33
3.15
Problem: Cyclotron Frequency
34
3.16
Problem:
deHaas-
Van
Alphen
34
3.17
Problem: Fermi Energy
34
4
Density of States
35
4.1
Problem: Density of States
37
4.2
Problem: Two-Dimensional Density of States
38
4.2
Problem: Two-Dimensional Tight Binding
38
4.4
Problem: Quasi-One-Dimensional Metal
38
4.5
Problem: Crossover to Quasi-One-Dimensional Metal
39
4.6
Problem: Phonon Mode of Two-Dimensional System
39
4.7
Problem: Saddle Point
40
4.8
Problem: Density of States in Superconductors
40
4.9
Problem: Energy Gap
41
4.10
Problem: Density of States for Hybridized Bands
41
4.11
Problem: Infinite-Dimensional DOS
41
4.12
Problem: Two-Dimensional Electron Gas
42
5
Elementary Excitations
43
5.1
Problem: Tight-Binding Model
46
5.2
Problem: Hybridization of Energy Bands
46
5.3
Problem:
Polarons
47
Contents
vii
5.4 Problem: Poiaritons 47
5.5 Problem:
Excitons
48
5.6 Problem: Holstein-Primakoff Transformation 48
5.7 Problem: Dyson-Maleev
Representation
48
5.8 Problem:
Spin Waves
49
5.9 Problem:
Spin Waves Again
49
5.10 Problem: Anisotropie Heisenberg Model 49
5.11 Problem: Solitons 50
6
Thermodynamics of
Noninteracting
Quasipartides
53
6.1 Problem:
Specific Heat of
Metals
and Insulators
60
6.2
Problem: Number of Phonons
60
6.3
Problem: Energy of the Phonon Gas
60
6.4
Problem: Bulk Modulus of Phonon Gas
60
6.5
Problem: Phonons in One Dimension
60
6.6
Problem: Electron-Hole Symmetry
61
6.7
Problem: Entropy of the Noninteracting Electron Gas
61
6.8
Problem: Free Energy with Gap at the Fermi Energy
61
6.9
Problem: Bulk Modulus at T=
0 62
6.10
Problem: Temperature Dependence of the Bulk Modulus
62
6.11
Problem: Chemical Potential of the Free-Electron Gas
62
6.12
Problem: EuO Specific Heat
62
6.13
Problem: Magnetization at Low Temperatures
62
6.14
Problem: Electronic Specific Heat
63
6.15
Problem: Quantum Hall Effect
63
7
Transport Properties
65
7.1
Problem: Temperature Dependent Resistance
72
7.2
Problem: Conductivity Tensor
72
7.3
Problem: Montgomery Method
73
7.4
Problem:
Anisotropie
Layer
73
7.5
Problem; Two-Charge-Carrier
Drude
Model
74
7.6
Problem: Thermal Conductivity
74
7.7
Problem: Residual Resistivity
74
7.8
Problem: Electric and Heat Transport
75
7.9
Problem: Conductivity of Tight-Binding Band
75
7.10
Problem: Hall Effect in Two-Dimensional Metals
75
7.11
Problem: Free-Electron Results from the Boltzmann Equations
76
7.12
Problem:
p
-п
Junctions
76
8
Optical Properties
79
8.1
Problem: Fourier Transform Infrared Spectroscopy
86
8.2
Problem: Optical Mode of KBr
87
viii Contents
8.3
Problem:
Direct-Gap
Semiconductor
87
8.4
Problem:
Inversion Symmetry
87
8.5
Problem:
Frequency-Dependent Conductivity
87
8.6
Problem: Frequency-Dependent Response of a Superconductor
88
8.7
Problem: Transmission of a Thin Superconductor
88
8.8
Problem: Bloch Oscillations
88
9
Interactions and Phase Transitions
91
9.1
Problem: Spontaneous Polarization
95
9.2
Problem: Divergent Susceptibility
96
9.3
Problem: Large-U Hubbard Model
96
9.4
Problem: Infinite Range Hubbard Model
97
9.5
Problem:
Stoner
Model
97
9.6
Problem: One-Dimensional Electron System
98
9.7
Problem: Peierls Distortion
98
9.8
Problem: Singularity at 2kv
99
9.9
Problem: Susceptibility of a One-Dimensional Electron Gas
99
9.10
Problem: Critical Temperature in Mean Field Approximation
99
9.11
Problem: Instability of Half-Filled Band
99
9.12
Problem: Screening of an Impurity Charge
100
9.13
Problem: Fermi Surface Nesting in Two Dimensions
100
9.14
Problem: Fermi Surface Nesting in Quasi One Dimension
101
9.15
Problem: Anderson Model
101
PART II SOLUTIONS TO PROBLEMS
1
Crystal Structures
107
1.1
Solution: Symmetries
107
1.2
Solution: Rotations
108
1.3
Solution: Copper Oxide Layers
108
1.4
Solution: Graphite
109
1.5
Solution: Structure of ArC60
109
1.6
Solution: hep
гпа/сс
Structures
111
1.7
Solution: hep and bec Structures
112
1.8
Solution: Structure Factor of AVC6O
112
1.9
Solution: Neutron Diffraction Device
113
1.10
Solution: Linear Array of Emitters, Finite Size Effects
114
1.11
Solution: Linear Array of Emitters,
Superlattice 115
1.12
Solution: Powder Diffraction of hep ana fee Crystals
116
1.13
Solution: Momentum Resolution
117
1.14
Solution: Finite Size Effects
119
1.15
Solution: Random Displacement
120
Contents
¡χ
1.16
Hint: Vacancies
121
1.17
Hint: Integrated Scattering Intensity
122
2
Interatomic Forces, Lattice Vibrations
123
2.1
Solution: Madelung Constant
123
2.2
Solution: NaCI Bulk Modulus
125
2.3
Hint: Madelung with Screened Potential
127
2.4
Solution: Triple-axis Spectrometer
127
2.5
Solution: Phonons in Silicon
127
2.6
Solution: Linear Array of Emitters, Phonons
128
2.7
Hint: Long Range Interaction
128
2.8
Solution: Mass Defect
129
2.9
Solution: Debye Frequency
130
2.10
Solution: Vibrations of a Square Lattice
131
2.11
Solution:
Grüneisen
Parameter
133
2.12
Solution: Diatomic Chain
134
2.13
Hint: Damped Oscillation
135
2.14
Solution: Two-Dimensional Debye
136
2.15
Solution: Soft Optical Phonons
137
2.16
Hint: Soft Phonons Again
139
3
Electronic Band Structure
141
3.1
Solution: Nearly Free Electrons in One Dimension
141
3.2
Solution: Nearly Free Electrons in Dirac-Delta Potentials
141
3.3
Solution: Tight-Binding in Dirac-Delta Potentials
142
3.4
Solution: Dirac-Delta Potentials
143
3.5
Solution: Band Overlap
147
3.6
Solution: Nearly Free Electrons in Two Dimensions
147
3.7
Solution: Nearly Free Electron Bands
149
3.8
Solution: Instability at the Fermi Wavenumber
150
3.9
Solution: Electrons in 2D Nearly Free Electron Band
152
3.10
Solution: Square Lattice
153
3.11
Solution: Tight-Binding Band in Two Dimensions
154
3.12
Solution: Electrons in 2D Tight-Binding Band
156
3.13
Solution: Dirac-Delta Potentials in Two Dimensions
156
3.14
Hint: Effective Mass
157
3.15
Hint: Cyclotron Frequency
158
3.16
Solution:
deHaas-
Van
Alphen
159
3.17
Hint: Fermi Energy
159
4
Density of States
161
4.1
Solution: Density of States
161
4.2
Solution: Two-Dimensional Density of States
161
χ
Contents
4.3
Solution:
Two-Dimensional
Tight-Binding
162
4.4
Solution: Quasi-One-Dimensional Metal
163
4.5
Solution: Crossover to Quasi-One-Dimensional Metal
165
4.6
Solution: Phonon Mode of Two-Dimensional System
167
4.7
Solution: Saddle Point
168
4.8
Solution: Density of States in Superconductors
170
4.9
Solution: Energy Gap
171
4.10
Solution: Density of States for Hybridized Bands
171
4.11
Solution: Infinite-Dimensional DOS
172
4.12
Solution: Two-Dimensional Electron Gas
173
5
Elementary Excitations
175
5.1
Solution: Tight-Binding Model
175
5.2
Solution: Hybridization of Energy Bands
177
5.3
Solution:
Polarons
179
5.4
Solution: Polaritons
181
5.5
Hint:
Excitons
182
5.6
Solution: Holstein-Primakov Transformation
182
5.7
Hint: Dyson-Maleev Representation
183
5.8
Solutions: Spin Waves
183
5.9
Solution: Spin Waves Again
184
5.10
Solution:
Anisotropie Heisenberg
Model
185
5.11
Hint:
Solitons 186
6
Thermodynamics of Noninteracting Quasiparticles
187
6.1
Solution: Specific Heat of Metals and Insulators
187
6.2
Solution: Number of Phonons
188
6.3
Solution: Energy of the Phonon Gas
189
6.4
Solution: Bulk Modulus of Phonon Gas
190
6.5
Hint: Phonons in One Dimension
191
6.6
Solution: Electron-Hole Symmetry
191
6.7
Solution: Entropy of the Noninteracting Electron Gas
193
6.8
Solution: Free Energy with Gap at the Fermi Energy
194
6.9
Solution: Bulk Modulus at T=
0 195
6.10
Solution: Temperature Dependence of the Bulk Modulus
195
6.11
Solution: Chemical Potential of the Free-Electron Gas
197
6.12
Solution: EuO Specific Heat
198
6.13
Hint: Magnetization at Low Temperatures
199
6.14
Solution: Electronic Specific Heat
200
6.15
Solution: Quantum Hall Effect
201
7
Transport Properties
203
7.1
Solution: Temperature Dependent Resistance
203
7.2
Solution: Conductivity Tensor
204
Contents xi
7.3
Solution:
Montgomery Method
205
7.4
Solution:
Anisotropie
Layer
206
7.5
Solution: Two-Charge-Carrier
Drude
Model
207
7.6
Solution: Thermal Conductivity
209
7.7
Hint: Residual Resistivity
210
7.8
Solution: Electric and Heat Transport
210
7.9
Solution: Conductivity of Tight-Binding Band
212
7.10
Solution: Hall Effect in Two-Dimensional Metals
214
7.1
1 Solution: Free-Electron Results from the Boltzmann
Equations
215
7.12
Solution:
p
-п
Junctions
217
8
Optical Properties
219
8.1
Solution: Fourier Transform Infrared Spectroscopy
219
8.2
Solution: Optical Mode of KBr
220
8.3
Solution: Direct-Gap Semiconductor
220
8.4
Solution: Inversion Symmetry
222
8.5
Solution: Frequency-Dependent Conductivity
223
8.6
Solution: Frequency-Dependent Response of a Superconductor
226
8.7
Solution: Transmission of a Thin Superconductor
227
8.8
Solution: Bloch Oscillations
228
9
Interactions and Phase Transitions
231
9.1
Solution: Spontaneous Polarization
231
9.2
Solution: Divergent Susceptibility
232
9.3
Solution: Large-U Hubbard Model
233
9.4
Solution: Infinite Range Hubbard Model
236
9.5
Hint:
Stoner
Model
237
9.6
Solution: One-Dimensional Electron System
237
9.7
Solution: Peirerls Distortion
239
9.8
Hint: Singularity at 2*F
240
9.9
Solution: Susceptibility of a One-Dimensional Electron Gas
241
9.10
Solution: Critical Temperature in Mean Field Approximation
242
9.11
Solution: Instability of Half-Filled Band
242
9.12
Solution: Screening of an Impurity Charge
243
9.13
Solution: Fermi Surface Nesting in Two Dimensions
245
9.14
Solution: Fermi Surface Nesting in Quasi One Dimension
247
9.15
Solution: Anderson Model
249
References
253
Index
255
|
| adam_txt |
Contents
Preface
xiii
PART I PROBLEMS
1
Crystal Structures
3
1.1
Problem: Symmetries
9
1.2
Problem: Rotations
9
1.3
Problem: Copper Oxide Layers
10
1.4
Problem: Graphite
11
1.5
Problem: Structure of AxC60
11
1.6
Problem: hep and fee Structures
11
1.7
Problem: hep and bee Structures
11
1.8
Problem: Structure Factor of
АлС60
11
1.9
Problem: Neutron Diffraction Device
12
1.10
Problem: Linear Array of Emitters, Finite Size Effects
12
1.11
Problem: Linear Array of Emitters,
Superlattice 12
1.12
Problem: Powder Diffraction of hep and./cc Crystals
13
1.13
Problem: Momentum Resolution
13
1.14
Problem: Finite Size Effects
13
1.15
Problem: Random Displacement
13
1.16
Problem: Vacancies
14
1.17
Problem: Integrated Scattering Intensity
14
2
Interatomic Forces, Lattice Vibrations
15
2.1
Problem: Madelung Constant
19
2.2
Problem: NaCl Bulk Modulus
19
2.3
Problem: Madelung with Screened Potential
19
2.4
Problem: Triple-axis Spectrometer
20
2.5
Problem: Phonons in Silicon
20
2.6
Problem: Linear Array of Emitters, Phonons
20
2.7
Problem: Long Range Interaction
21
2.8
Problem: Mass Defect
21
2.9
Problem: Debye Frequency
21
2.10
Problem:
Vibrationsofa
Square Lattice
22
vi
Contents
2.11 Problem: Grüneisen Parameter 22
2.12 Problem:
Diatomic
Chain 22
2.13 Problem:
Damped Oscillation
22
2.14 Problem:
Two-Dimensional Debye
23
2.15 Problem:
Soft Optical Phonons
23
2.16
Problem: Soft Phonons Again
23
3
Electronic Band Structure
25
3.1
Problem: Nearly Free Electrons in One Dimension
30
3.2
Problem: Nearly Free Electrons in Dirac-Delta Potentials
30
3.3
Problem: Tight-Binding in Dirac-Delta Potentials
30
3.4
Problem: Dirac-Delta Potentials
31
3.5
Problem: Band Overlap
31
3.6
Problem: Nearly Free Electrons in Two Dimensions
31
3.7
Problem: Nearly Free Electron Bands
32
3.8
Problem: Instability at the Fermi Wavenumber
32
3.9
Problem: Electrons in 2D Nearly Free Electron Band
32
3.10
Problem: Square Lattice
32
3.11
Problem: Tight-Binding Band in Two Dimensions
33
3.12
Problem: Electrons in 2D Tight-Binding Band
33
3.13
Problem: Dirac-Delta Potentials in Two Dimensions
33
3.14
Problem: Effective Mass
33
3.15
Problem: Cyclotron Frequency
34
3.16
Problem:
deHaas-
Van
Alphen
34
3.17
Problem: Fermi Energy
34
4
Density of States
35
4.1
Problem: Density of States
37
4.2
Problem: Two-Dimensional Density of States
38
4.2
Problem: Two-Dimensional Tight Binding
38
4.4
Problem: Quasi-One-Dimensional Metal
38
4.5
Problem: Crossover to Quasi-One-Dimensional Metal
39
4.6
Problem: Phonon Mode of Two-Dimensional System
39
4.7
Problem: Saddle Point
40
4.8
Problem: Density of States in Superconductors
40
4.9
Problem: Energy Gap
41
4.10
Problem: Density of States for Hybridized Bands
41
4.11
Problem: Infinite-Dimensional DOS
41
4.12
Problem: Two-Dimensional Electron Gas
42
5
Elementary Excitations
43
5.1
Problem: Tight-Binding Model
46
5.2
Problem: Hybridization of Energy Bands
46
5.3
Problem:
Polarons
47
Contents
vii
5.4 Problem: Poiaritons 47
5.5 Problem:
Excitons
48
5.6 Problem: Holstein-Primakoff Transformation 48
5.7 Problem: Dyson-Maleev
Representation
48
5.8 Problem:
Spin Waves
49
5.9 Problem:
Spin Waves Again
49
5.10 Problem: Anisotropie Heisenberg Model 49
5.11 Problem: Solitons 50
6
Thermodynamics of
Noninteracting
Quasipartides
53
6.1 Problem:
Specific Heat of
Metals
and Insulators
60
6.2
Problem: Number of Phonons
60
6.3
Problem: Energy of the Phonon Gas
60
6.4
Problem: Bulk Modulus of Phonon Gas
60
6.5
Problem: Phonons in One Dimension
60
6.6
Problem: Electron-Hole Symmetry
61
6.7
Problem: Entropy of the Noninteracting Electron Gas
61
6.8
Problem: Free Energy with Gap at the Fermi Energy
61
6.9
Problem: Bulk Modulus at T=
0 62
6.10
Problem: Temperature Dependence of the Bulk Modulus
62
6.11
Problem: Chemical Potential of the Free-Electron Gas
62
6.12
Problem: EuO Specific Heat
62
6.13
Problem: Magnetization at Low Temperatures
62
6.14
Problem: Electronic Specific Heat
63
6.15
Problem: Quantum Hall Effect
63
7
Transport Properties
65
7.1
Problem: Temperature Dependent Resistance
72
7.2
Problem: Conductivity Tensor
72
7.3
Problem: Montgomery Method
73
7.4
Problem:
Anisotropie
Layer
73
7.5
Problem; Two-Charge-Carrier
Drude
Model
74
7.6
Problem: Thermal Conductivity
74
7.7
Problem: Residual Resistivity
74
7.8
Problem: Electric and Heat Transport
75
7.9
Problem: Conductivity of Tight-Binding Band
75
7.10
Problem: Hall Effect in Two-Dimensional Metals
75
7.11
Problem: Free-Electron Results from the Boltzmann Equations
76
7.12
Problem:
p
-п
Junctions
76
8
Optical Properties
79
8.1
Problem: Fourier Transform Infrared Spectroscopy
86
8.2
Problem: Optical Mode of KBr
87
viii Contents
8.3
Problem:
Direct-Gap
Semiconductor
87
8.4
Problem:
Inversion Symmetry
87
8.5
Problem:
Frequency-Dependent Conductivity
87
8.6
Problem: Frequency-Dependent Response of a Superconductor
88
8.7
Problem: Transmission of a Thin Superconductor
88
8.8
Problem: Bloch Oscillations
88
9
Interactions and Phase Transitions
91
9.1
Problem: Spontaneous Polarization
95
9.2
Problem: Divergent Susceptibility
96
9.3
Problem: Large-U Hubbard Model
96
9.4
Problem: Infinite Range Hubbard Model
97
9.5
Problem:
Stoner
Model
97
9.6
Problem: One-Dimensional Electron System
98
9.7
Problem: Peierls Distortion
98
9.8
Problem: Singularity at 2kv
99
9.9
Problem: Susceptibility of a One-Dimensional Electron Gas
99
9.10
Problem: Critical Temperature in Mean Field Approximation
99
9.11
Problem: Instability of Half-Filled Band
99
9.12
Problem: Screening of an Impurity Charge
100
9.13
Problem: Fermi Surface Nesting in Two Dimensions
100
9.14
Problem: Fermi Surface Nesting in Quasi One Dimension
101
9.15
Problem: Anderson Model
101
PART II SOLUTIONS TO PROBLEMS
1
Crystal Structures
107
1.1
Solution: Symmetries
107
1.2
Solution: Rotations
108
1.3
Solution: Copper Oxide Layers
108
1.4
Solution: Graphite
109
1.5
Solution: Structure of ArC60
109
1.6
Solution: hep
гпа/сс
Structures
111
1.7
Solution: hep and bec Structures
112
1.8
Solution: Structure Factor of AVC6O
112
1.9
Solution: Neutron Diffraction Device
113
1.10
Solution: Linear Array of Emitters, Finite Size Effects
114
1.11
Solution: Linear Array of Emitters,
Superlattice 115
1.12
Solution: Powder Diffraction of hep ana fee Crystals
116
1.13
Solution: Momentum Resolution
117
1.14
Solution: Finite Size Effects
119
1.15
Solution: Random Displacement
120
Contents
¡χ
1.16
Hint: Vacancies
121
1.17
Hint: Integrated Scattering Intensity
122
2
Interatomic Forces, Lattice Vibrations
123
2.1
Solution: Madelung Constant
123
2.2
Solution: NaCI Bulk Modulus
125
2.3
Hint: Madelung with Screened Potential
127
2.4
Solution: Triple-axis Spectrometer
127
2.5
Solution: Phonons in Silicon
127
2.6
Solution: Linear Array of Emitters, Phonons
128
2.7
Hint: Long Range Interaction
128
2.8
Solution: Mass Defect
129
2.9
Solution: Debye Frequency
130
2.10
Solution: Vibrations of a Square Lattice
131
2.11
Solution:
Grüneisen
Parameter
133
2.12
Solution: Diatomic Chain
134
2.13
Hint: Damped Oscillation
135
2.14
Solution: Two-Dimensional Debye
136
2.15
Solution: Soft Optical Phonons
137
2.16
Hint: Soft Phonons Again
139
3
Electronic Band Structure
141
3.1
Solution: Nearly Free Electrons in One Dimension
141
3.2
Solution: Nearly Free Electrons in Dirac-Delta Potentials
141
3.3
Solution: Tight-Binding in Dirac-Delta Potentials
142
3.4
Solution: Dirac-Delta Potentials
143
3.5
Solution: Band Overlap
147
3.6
Solution: Nearly Free Electrons in Two Dimensions
147
3.7
Solution: Nearly Free Electron Bands
149
3.8
Solution: Instability at the Fermi Wavenumber
150
3.9
Solution: Electrons in 2D Nearly Free Electron Band
152
3.10
Solution: Square Lattice
153
3.11
Solution: Tight-Binding Band in Two Dimensions
154
3.12
Solution: Electrons in 2D Tight-Binding Band
156
3.13
Solution: Dirac-Delta Potentials in Two Dimensions
156
3.14
Hint: Effective Mass
157
3.15
Hint: Cyclotron Frequency
158
3.16
Solution:
deHaas-
Van
Alphen
159
3.17
Hint: Fermi Energy
159
4
Density of States
161
4.1
Solution: Density of States
161
4.2
Solution: Two-Dimensional Density of States
161
χ
Contents
4.3
Solution:
Two-Dimensional
Tight-Binding
162
4.4
Solution: Quasi-One-Dimensional Metal
163
4.5
Solution: Crossover to Quasi-One-Dimensional Metal
165
4.6
Solution: Phonon Mode of Two-Dimensional System
167
4.7
Solution: Saddle Point
168
4.8
Solution: Density of States in Superconductors
170
4.9
Solution: Energy Gap
171
4.10
Solution: Density of States for Hybridized Bands
171
4.11
Solution: Infinite-Dimensional DOS
172
4.12
Solution: Two-Dimensional Electron Gas
173
5
Elementary Excitations
175
5.1
Solution: Tight-Binding Model
175
5.2
Solution: Hybridization of Energy Bands
177
5.3
Solution:
Polarons
179
5.4
Solution: Polaritons
181
5.5
Hint:
Excitons
182
5.6
Solution: Holstein-Primakov Transformation
182
5.7
Hint: Dyson-Maleev Representation
183
5.8
Solutions: Spin Waves
183
5.9
Solution: Spin Waves Again
184
5.10
Solution:
Anisotropie Heisenberg
Model
185
5.11
Hint:
Solitons 186
6
Thermodynamics of Noninteracting Quasiparticles
187
6.1
Solution: Specific Heat of Metals and Insulators
187
6.2
Solution: Number of Phonons
188
6.3
Solution: Energy of the Phonon Gas
189
6.4
Solution: Bulk Modulus of Phonon Gas
190
6.5
Hint: Phonons in One Dimension
191
6.6
Solution: Electron-Hole Symmetry
191
6.7
Solution: Entropy of the Noninteracting Electron Gas
193
6.8
Solution: Free Energy with Gap at the Fermi Energy
194
6.9
Solution: Bulk Modulus at T=
0 195
6.10
Solution: Temperature Dependence of the Bulk Modulus
195
6.11
Solution: Chemical Potential of the Free-Electron Gas
197
6.12
Solution: EuO Specific Heat
198
6.13
Hint: Magnetization at Low Temperatures
199
6.14
Solution: Electronic Specific Heat
200
6.15
Solution: Quantum Hall Effect
201
7
Transport Properties
203
7.1
Solution: Temperature Dependent Resistance
203
7.2
Solution: Conductivity Tensor
204
Contents xi
7.3
Solution:
Montgomery Method
205
7.4
Solution:
Anisotropie
Layer
206
7.5
Solution: Two-Charge-Carrier
Drude
Model
207
7.6
Solution: Thermal Conductivity
209
7.7
Hint: Residual Resistivity
210
7.8
Solution: Electric and Heat Transport
210
7.9
Solution: Conductivity of Tight-Binding Band
212
7.10
Solution: Hall Effect in Two-Dimensional Metals
214
7.1
1 Solution: Free-Electron Results from the Boltzmann
Equations
215
7.12
Solution:
p
-п
Junctions
217
8
Optical Properties
219
8.1
Solution: Fourier Transform Infrared Spectroscopy
219
8.2
Solution: Optical Mode of KBr
220
8.3
Solution: Direct-Gap Semiconductor
220
8.4
Solution: Inversion Symmetry
222
8.5
Solution: Frequency-Dependent Conductivity
223
8.6
Solution: Frequency-Dependent Response of a Superconductor
226
8.7
Solution: Transmission of a Thin Superconductor
227
8.8
Solution: Bloch Oscillations
228
9
Interactions and Phase Transitions
231
9.1
Solution: Spontaneous Polarization
231
9.2
Solution: Divergent Susceptibility
232
9.3
Solution: Large-U Hubbard Model
233
9.4
Solution: Infinite Range Hubbard Model
236
9.5
Hint:
Stoner
Model
237
9.6
Solution: One-Dimensional Electron System
237
9.7
Solution: Peirerls Distortion
239
9.8
Hint: Singularity at 2*F
240
9.9
Solution: Susceptibility of a One-Dimensional Electron Gas
241
9.10
Solution: Critical Temperature in Mean Field Approximation
242
9.11
Solution: Instability of Half-Filled Band
242
9.12
Solution: Screening of an Impurity Charge
243
9.13
Solution: Fermi Surface Nesting in Two Dimensions
245
9.14
Solution: Fermi Surface Nesting in Quasi One Dimension
247
9.15
Solution: Anderson Model
249
References
253
Index
255 |
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| any_adam_object_boolean | 1 |
| author | Mihály, László 1949- Martin, Michael C. |
| author_GND | (DE-588)13669411X (DE-588)137007213 |
| author_facet | Mihály, László 1949- Martin, Michael C. |
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| author_sort | Mihály, László 1949- |
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| building | Verbundindex |
| bvnumber | BV023241786 |
| classification_rvk | UP 1050 |
| classification_tum | PHY 601f PHY 003f |
| ctrlnum | (OCoLC)634720012 (DE-599)BVBBV023241786 |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV023241786 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:24:02Z |
| indexdate | 2024-07-09T21:13:54Z |
| institution | BVB |
| isbn | 9780471152873 0471152870 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016427323 |
| oclc_num | 634720012 |
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| physical | XIV, 261 S. Ill., graph. Darst. - Ill., graph. Darst. |
| publishDate | 2004 |
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| spelling | Mihály, László 1949- Verfasser (DE-588)13669411X aut Solid state physics problems and solutions László Mihály ; Michael C. Martin Weinheim Wiley 2004 XIV, 261 S. Ill., graph. Darst. - Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics textbook Festkörperphysik (DE-588)4016921-2 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Festkörperphysik (DE-588)4016921-2 s DE-604 Martin, Michael C. Verfasser (DE-588)137007213 aut Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016427323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mihály, László 1949- Martin, Michael C. Solid state physics problems and solutions Festkörperphysik (DE-588)4016921-2 gnd |
| subject_GND | (DE-588)4016921-2 (DE-588)4143389-0 |
| title | Solid state physics problems and solutions |
| title_auth | Solid state physics problems and solutions |
| title_exact_search | Solid state physics problems and solutions |
| title_exact_search_txtP | Solid state physics problems and solutions |
| title_full | Solid state physics problems and solutions László Mihály ; Michael C. Martin |
| title_fullStr | Solid state physics problems and solutions László Mihály ; Michael C. Martin |
| title_full_unstemmed | Solid state physics problems and solutions László Mihály ; Michael C. Martin |
| title_short | Solid state physics |
| title_sort | solid state physics problems and solutions |
| title_sub | problems and solutions |
| topic | Festkörperphysik (DE-588)4016921-2 gnd |
| topic_facet | Festkörperphysik Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016427323&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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