Solid state physics: problems and solutions
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| Format: | Book |
| Language: | English |
| Published: |
Weinheim
WILEY-VCH
2009
|
| Edition: | 2., rev. and enl. ed. |
| Series: | Physics textbook
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| Subjects: | |
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| Physical Description: | XVIII, 315 S. graph. Darst. |
| ISBN: | 9783527408559 |
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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 Laszlo Mihaly ; Michael C. Martin |
| 250 | |a 2., rev. and enl. ed. | ||
| 264 | 1 | |a Weinheim |b WILEY-VCH |c 2009 | |
| 300 | |a XVIII, 315 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Physics textbook | |
| 650 | 4 | |a Solid state physics | |
| 650 | 4 | |a Solid state physics |v Problems, exercises, etc | |
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| 655 | 7 | |0 (DE-588)4143389-0 |a Aufgabensammlung |2 gnd-content | |
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Contents
Preface
to the Second Edition XV
Preface to the First Edition
XVII
Part I Problems
1
1
Crystal Structures
3
1.1
Problem: Symmetries
8
1.2
Problem: Rotations
8
1.3
Problem: Copper Oxide Layers
9
1.4
Problem: Graphite
10
1.5
Problem: Structure of AxC60
10
1.6
Problem: hep and jec Structures
10
1.7
Problem: hep and bec Structures
2 2
1.8
Problem: Structure Factor of AxC60
11
1.9
Problem: Neutron Diffraction Device
11
1.10
Problem: Linear Array of Emitters: Finite Size Effects
11
1.11
Problem: Linear Array of Emitters:
Superlattice 12
1.12
Problem: Powder Diffraction of hep and fee Crystals
12
1.13
Problem: Momentum Resolution
12
1.14
Problem: Finite Size Effects
12
1.15
Problem: Random Displacement
13
1.16
Problem: Vacancies
13
1.17
Problem: Integrated Scattering Intensity
13
2
Interatomic Forces and 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
19
2.5
Problem: Phonons in Silicon
20
2.6
Problem: Linear Array of Emitters." Phonons
20
VI Contents
2.7
Problem: Long-range Interaction
21
2.8
Problem: Mass Defect
21
2.9
Problem: Debye Frequency
21
2.10
Problem: Vibrations of a Square Lattice
21
2.11
Problem:
Grüneisen
Parameter
22
2.12
Problem: Diatomic Chain
22
2.13
Problem: Damped Oscillation
23
2.14
Problem: Two-dimensional Debye
23
2.15
Problem: Soft Optical Phonons
23
2.16
Problem: Soft Phonons Again
23
2.17
Problem: Nanowire Phonons
24
3
Electronic Band Structure
25
3.1
Problem: Nearly Free Electrons in One Dimension
30
3.2
Problem: Eigenfunctions of Nearly Free Electrons in One
Dimension
30
3.3
Problem: Tight-binding Hamiltonian
31
3.4
Problem: Nearly Free Electrons in Dirac-delta Potentials
31
3.5
Problem: Tight-binding in Dirac-delta Potentials
31
3.6
Problem: Dirac-delta Potentials
32
3.7
Problem: Band Overlap
32
3.8
Problem: Nearly Free Electrons in Two Dimensions
32
3.9
Problem: Nearly Free-electron Bands
33
3.10
Problem: Instability at the Fermi Wavenumber
33
3.11
Problem: Electrons in 2D Nearly Free-electron Band
33
3.12
Problem: Square Lattice
34
3.13
Problem: Tight-binding Band in Two Dimensions
34
3.14
Problem: Electrons in 2D Tight-binding Band
34
3.15
Problem: Dirac-delta Potentials in Two Dimensions
34
3.16
Problem: Graphene
35
3.17
Problem: Effective Mass
35
3.18
Problem: Cyclotron Frequency
35
3.19
Problem:
de Haas-van Alphen
35
3.20
Problem: Fermi Energy
36
4
Density of States
37
4.1
Problem: Density of States
39
4.2
Problem: Two-dimensional Density of States
40
4.3
Problem: Two-dimensional Tight Binding
40
4.4
Problem: Tight Binding from One to Three Dimensions
40
4.5
Problem: Crossover to Quasi-one-dimensional Metal
41
4.6
Problem: Phonon Mode of Two-dimensional System
42
4.7
Problem: Saddle Point
42
4.8
Problem: Density of States in Superconductors
43
4.9
Problem: Energy Gap
43
Contents
VII
4.10 Problem:
Density of States for Hybridized Bands
43
4.11
Problem: Infinite-dimensional DOS
44
4.12
Problem: Two-to Three-dimensional Crossover
44
4.13
Problem: One-to Two-dimensional Crossover
45
4.14
Problem: Carbon Nanotube
45
5
Elementary Excitations
47
5.1
Problem: Tight-binding Model
50
5.2
Problem: Impurity State in the One-dimensional Tight-binding
Model
51
5.3
Problem: Hybridization of Energy Bands
51
5.4
Problem:
Polarons
52
5.5
Problem: Polaritons
52
5.6
Problem:
Excitons
52
5.7
Problem:
Holstein-PrimakofF
Transformation
53
5.8
Problem: Dyson-Maleev Representation
53
5.9
Problem: Spin Waves
53
5.10
Problem: Spin Waves Again
54
5.11
Problem:
Anisotropie Heisenberg
Model
54
5.12
Problem:
Solitons 54
5.13
Problem: Dirac
Fermions
in Graphene
56
6
Thermodynamics of Noninteracting Quasiparticles
57
6.1
Problem: Specific Heat of Metals and Insulators
64
6.2
Problem: Number of Phonons
64
6.3
Problem: Energy of the Phonon Gas
64
6.4
Problem: Bulk Modulus of the Phonon Gas
64
6.5
Problem: Phonons in One Dimension
64
6.6
Problem: Electron-Hole Symmetry
65
6.7
Problem: Entropy of the Noninteracting Electron Gas
65
6.8
Problem: Free Energy with Gap at the Fermi Energy
65
6.9
Problem: Bulk Modulus at
Γ
= 0 66
6.10
Problem: Temperature Dependence of the Bulk Modulus
66
6.11
Problem: Chemical Potential of the Free-electron Gas
66
6.12
Problem: EuO Specific Heat
66
6.13
Problem: Magnetization at Low Temperatures
66
6.14
Problem: Electronic Specific Heat
66
6.15
Problem: Quantum Hall Effect
67
7
Transport Properties
69
7.1
Problem: Temperature-dependent Resistance
76
7.2
Problem: Conductivity Tensor
76
7.3
Problem: Montgomery' Method
76
7.4
Problem:
Anisotropie
Layer
77
7.5
Problem: Two-charge-carrier
Drude
Model
78
VIII Contents
7.6
Problem:
Thermal
Conductivity
78
7.7
Problem: Residual Resistivity
78
7.8
Problem: Electric and Heat Transport
79
7.9
Problem: Conductivity of Tight-binding Band
79
7.10
Problem: Hall Effect in Two-dimensional Metals
80
7.11
Problem: Free-electron Results from the Boltzmann Equations
80
7.12
Problem:
p
-п
Junctions
80
7.13
Problem: Mott-Ioffe-Regel
81
8
Optical Properties
83
8.1
Problem: Reflectivity and Transmission: Multiple Interfaces
93
8.2
Problem: Group Velocity
93
8.3
Problem: Tinkham Formula
94
8.4
Problem: Transmission of a Thin Superconductor
94
8.5
Problem: Fourier Transform Infrared Spectroscopy
95
8.6
Problem: Sum Rule: Dielectric Constant
96
8.7
Problem: Optical Mode of KBr
96
8.8
Problem: Direct-gap Semiconductor
96
8.9
Problem: Inversion Symmetry
97
8.10
Problem: Frequency-dependent Conductivity
97
8.11
Problem: Frequency-dependent Response of a Superconductor
97
8.12
Problem: Optical Conductivity Tensor
98
8.13
Problem: Joint Density of States in One Dimension
98
8.14
Problem: One-dimensional Semiconductor
98
8.15
Problem: Conductivity of Graphene
99
8.16
Problem:
Biodi
Oscillations
99
9
Interactions and Phase Transitions
101
9.1
Problem: Spontaneous Polarization
205
9.2
Problem: Divergent Susceptibility
206
9.3
Problem: Large-U Hubbard Model
106
9.4
Problem: Infinite-range Hubbard Model
207
9.5
Problem:
Stoner
Model
107
9.6
Problem: One-dimensional Electron System
107
9.7
Problem: Peierls Distortion 20S
9.8
Problem: Singularity at 2kF
208
9.9
Problem: Susceptibility of a One-dimensional Electron Gas
209
9.10
Problem: Critical Temperature in Mean Field Approximation
209
9.11
Problem: Instability of Half-filled Band
209
9.12
Problem: Screening of an Impurity Charge
220
9.13
Problem: Fermi Surface Nesting in Two Dimensions
220
9.14
Problem: Fermi Surface Nesting in Quasi-one-dimension 111
9.15
Problem: Anderson Model
222
9.16
Problem: Collective Jahn-Teller Distortion
113
Contents
IX
ΊΟ
Mesoscopic and Nanoscale Systems 115
10.1 Problem: Differential
Conductance of
a
Tunnel
Junction
122
10.2 Problem: Sharvin
Formula
122
10.3 Problem:
Ballistic
Transport 123
10.4 Problem:
Tunneling from a Ballistic Conductor
123
10.5
Problem: Reflectivity of a Lattice Defect
124
10.6
Problem: Two Scatterers: Incoherent Propagation
125
10.7
Problem: Two Scatterers: Coherent Propagation
125
10.8
Problem: Strong Localization
126
10.9
Problem: Coulomb Blockade
126
10.10
Problem: Single-atom Transistor
127
Partii
Solutions to Problems
129
Π
Crystal Structures
131
11.1
Solution: Symmetries
131
11.2
Solution: Rotations
131
11.3
Solution: Copper Oxide Layers
132
11.4
Solution: Graphite
133
11.5
Solution: Structure of
АуСбо
133
11.6
Solution: hep
andate
Structures
134
11.7
Solution: hep and bee Structures
135
11.8
Solution: Structure Factor of AxC60
136
11.9
Solution: Neutron Diffraction Device
337
11.10
Solution: Linear Array of Emitters, Finite Size Effects
137
11.11
Solution: Linear Array of Emitters:
Superlattice 139
11.12
Solution: Powder Diffraction of hep and fee Crystals
140
11.13
Solution: Momentum Resolution
342
11.14
Solution: Finite Size Effects
143
11.15
Solution: Random Displacement
245
11.16
Hint: Vacancies
346
11.17
Hint: Integrated Scattering Intensity
246
12
Interatomic Forces and Lattice Vibrations
247
12.1
Solution: Madelung Constant
247
12.2
Solution: NaCl Bulk Modulus
149
12.3
Hint: Madelung with Screened Potential
252
12.4
Solution: Triple-axis Spectrometer
252
12.5
Solution: Phonons in Silicon
252
12.6
Solution: Linear Array of Emitters: Phonons
252
12.7
Hint: Long-range Interaction
252
12.8
Solution: Mass Defect
153
12.9
Solution: Debye Frequency
254
12.10
Solution: Vibrations of a Square Lattice
155
12.11
Solution:
Grüneisen
Parameter
256
Χ Ι
Contents
12.12
Solution: Diatomic Chain
157
12.13
Hint: Damped Oscillation
159
12.14
Solution: Two-dimensional Debye
159
12.15
Solution: Soft Optical Phonons
160
12.16
Hint: Soft Phonons Again
162
12.17
Solution: Nanowire Phonons
162
13
Electronic Band Structure
163
13.1
Solution: Nearly Free Electrons in One Dimension
163
13.2
Solution: Eigenfunctions of Nearly Free Electrons in One
Dimension
164
13.3
Solution: Tight-binding Hamiltonian
366
13.4
Solution: Nearly Free Electrons in Dirac-delta Potentials
166
13.5
Solution: Tight binding in Dirac-delta Potentials
166
13.6
Solution: Dirac-delta Potentials
168
13.7
Solution: Band Overlap
171
13.8
Solution: Nearly Free Electrons in Two Dimensions
172
13.9
Solution: Nearly Free-electron Bands
174
13.10
Solution: Instability at the Fermi Wavenumber
174
13.11
Solution: Electrons in 2D Nearly Free-electron Band
176
13.12
Solution: Square Lattice
178
13.13
Solution: Tight-binding Band in Two Dimensions
179
13.14
Solution: Electrons in 2D Tight-binding Band
180
13.15
Solution: Dirac-delta Potentials in Two Dimensions
181
13.16
Hint: Graphene
181
13.17
Hint: Effective Mass
182
13.18
Hint: Cyclotron Frequency
184
13.19
Solution:
de Haas-van Alphen
184
13.20
Hint: Fermi Energy
184
14
Density of States
187
14.1
Solution: Density of States
187
14.2
Solution: Two-dimensional Density of States
187
14.3
Solution: Two-dimensional Tight-binding
188
14.4
Solution: Tight-binding from One to Three Dimensions
189
14.5
Solution: Crossover to Quasi-one-dimensional Metal
191
14.6
Solution: Phonon Mode of Two-dimensional System
193
14.7
Solution: Saddle Point
194
14.8
Solution: Density of States in Superconductors
196
14.9
Solution: Energy Gap
397
14.10
Solution: Density of States for Hybridized Bands
197
14.11
Solution: Infinite-dimensional DOS
199
14.12
Solution: Two- to Three-dimensional Crossover
200
14.13
Solution: One-to Two-dimensional Crossover
201
14.14
Solution: Carbon Nanotube
202
Contents
XI
15
Elementary
Excitations
205
15.1
Solution:
Tight-binding Model
203
15.2
Solution:
Impurity
State
in the One-dimensional Tight-binding
Model
205
15.3
Solution: Hybridization of Energy Bands
206
15.4
Solution:
Polarons
208
15.5
Solution: Polaritons
210
15.6
Hint:
Excitons
211
15.7
Solution: Holstein-PrimakofFTransformation
212
15.8
Hint: Dyson-Maleev Representation
212
15.9
Solutions: Spin Waves
212
15.10
Solution: Spin Waves Again
214
15.11
Solution:
Anisotropie Heisenberg
Model
214
15.12
Hint:
Solitons 215
15.13
Solution: Dirac
Fermions
in Graphene
216
16
Thermodynamics of Noninteracting Quasiparticles
217
16.1
Solution: Specific Heat of Metals and Insulators
217
16.2
Solution: Number of Phonons
227
16.3
Solution: Energy of the Phonon Gas
238
16.4
Solution: Bulk Modulus of the Phonon Gas
220
16.5
Hint: Phonons in One Dimension
221
16.6
Solution: Electron-Hole Symmetry
221
16.7
Solution: Entropy of the Noninteracting Electron Gas
223
16.8
Solution: Free Energy with Gap at the Fermi Energy
224
16.9
Solution: Bulk Modulus at
Γ
= 0 226
16.10
Solution: Temperature Dependence of the Bulk Modulus
226
16.11
Solution: Chemical Potential of the Free-electron Gas
227
16.12
Solution: EuO Specific Heat
229
16.13
Hint: Magnetization at Low Temperatures
230
16.14
Solution: Electronic Specific Heat
230
16.15
Solution: Quantum Hall Effect
232
17
Transport Properties
235
17.1
Solution: Temperature-dependent Resistance
235
17.2
Solution: Conductivity Tensor
236
17.3
Solution: Montgomery Method
238
17.4
Solution:
Anisotropie
Layer
238
17.5
Solution: Two-charge-carrier
Drude
Model
240
17.6
Solution: Thermal Conductivity
242
17.7
Hint: Residual Resistivity
243
17.8
Solution: Electric and Heat Transport
243
17.9
Solution: Conductivity of Tight-binding Band
244
XII Contents
17.10
Solution: Hall
Effect in Two-dimensional Metals
246
17.11
Solution: Free-electron Results from the Boltzmann Equations
248
17.12
Solution:
p
-п
Junctions
250
17.13
Solution: Mott-Ioffe-Regel
251
18
Optical Properties
253
18.1
Solution: Reflectivity and Transmission: Multiple Interfaces
253
18.2
Solution: Group Velocity
254
18.3
Solution: Tinkham Formula
255
18.4
Solution: Transmission of a Thin Superconductor
256
18.5
Solution: Fourier Transform Infrared Spectroscopy
257
18.6
Solution: Sum Rule: Dielectric Constant
257
18.7
Solution: Optical Mode of KBr
257
18.8
Solution: Direct-gap Semiconductor
258
18.9
Solution: Inversion Symmetry
259
18.10
Solution: Frequency-dependent Conductivity
260
18.11
Solution: Frequency-dependent Response of a Superconductor
263
18.12
Solution: Optical Conductivity Tensor
264
18.13
Solution: Joint Density of States in One Dimension
265
18.14
Solution: One-dimensional Semiconductor
266
18.15
Solution: Conductivity of Graphene
268
18.16
Solution: Bloch Oscillations
269
19
Interactions and Phase Transitions
273
19.1
Solution: Spontaneous Polarization
273
19.2
Solution: Divergent Susceptibility
274
19.3
Solution: Large-U Hubbard Model
275
19.4
Solution: Infinite-range Hubbard Model
278
19.5
Hint:
Stoner
Model
279
19.6
Solution: One-dimensional Electron System
279
19.7
Solution: Peierls Distortion
281
19.8
Solution: Singularity at 2fcF
282
19.9
Solution: Susceptibility of a One-dimensional Electron Gas
283
19.10
Solution: Critical Temperature in Mean Field Approximation
284
19.11
Solution: Instability of Half-filled Band
284
19.12
Solution: Screening of an Impurity Charge
285
19.13
Solution: Fermi Surface Nesting in Two Dimensions
287
19.14
Solution: Fermi Surface Nesting in Quasi One Dimension
288
19.15
Solution: Anderson Model
291
19.16
Solution: Collective Jahn-Teller Distortion
294
20
Mesoscopic and
Nano-scale
Systems
297
20.1
Solution: Differential Conductance of a Tunnel Junction
297
20.2
Solution: Sharvin Formula
297
20.3
Solution: Ballistic Transport
298
Contents
XIII
20.4
Solution: Tunneling from a Ballistic Conductor
299
20.5
Solution: Reflectivity of a Lattice Defect
299
20.6
Solution: Two Scatterers: Incoherent Propagation
300
20.7
Solution: Two Scatterers: Coherent Propagation
301
20.8
Solution: Strong Localization
301
20.9
Solution: Coulomb Blockade
302
20.10
Solution: Single-atom Transistor
303
References
305
Index
307 |
| adam_txt |
Contents
Preface
to the Second Edition XV
Preface to the First Edition
XVII
Part I Problems
1
1
Crystal Structures
3
1.1
Problem: Symmetries
8
1.2
Problem: Rotations
8
1.3
Problem: Copper Oxide Layers
9
1.4
Problem: Graphite
10
1.5
Problem: Structure of AxC60
10
1.6
Problem: hep and jec Structures
10
1.7
Problem: hep and bec Structures
2 2
1.8
Problem: Structure Factor of AxC60
11
1.9
Problem: Neutron Diffraction Device
11
1.10
Problem: Linear Array of Emitters: Finite Size Effects
11
1.11
Problem: Linear Array of Emitters:
Superlattice 12
1.12
Problem: Powder Diffraction of hep and fee Crystals
12
1.13
Problem: Momentum Resolution
12
1.14
Problem: Finite Size Effects
12
1.15
Problem: Random Displacement
13
1.16
Problem: Vacancies
13
1.17
Problem: Integrated Scattering Intensity
13
2
Interatomic Forces and 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
19
2.5
Problem: Phonons in Silicon
20
2.6
Problem: Linear Array of Emitters." Phonons
20
VI Contents
2.7
Problem: Long-range Interaction
21
2.8
Problem: Mass Defect
21
2.9
Problem: Debye Frequency
21
2.10
Problem: Vibrations of a Square Lattice
21
2.11
Problem:
Grüneisen
Parameter
22
2.12
Problem: Diatomic Chain
22
2.13
Problem: Damped Oscillation
23
2.14
Problem: Two-dimensional Debye
23
2.15
Problem: Soft Optical Phonons
23
2.16
Problem: Soft Phonons Again
23
2.17
Problem: Nanowire Phonons
24
3
Electronic Band Structure
25
3.1
Problem: Nearly Free Electrons in One Dimension
30
3.2
Problem: Eigenfunctions of Nearly Free Electrons in One
Dimension
30
3.3
Problem: Tight-binding Hamiltonian
31
3.4
Problem: Nearly Free Electrons in Dirac-delta Potentials
31
3.5
Problem: Tight-binding in Dirac-delta Potentials
31
3.6
Problem: Dirac-delta Potentials
32
3.7
Problem: Band Overlap
32
3.8
Problem: Nearly Free Electrons in Two Dimensions
32
3.9
Problem: Nearly Free-electron Bands
33
3.10
Problem: Instability at the Fermi Wavenumber
33
3.11
Problem: Electrons in 2D Nearly Free-electron Band
33
3.12
Problem: Square Lattice
34
3.13
Problem: Tight-binding Band in Two Dimensions
34
3.14
Problem: Electrons in 2D Tight-binding Band
34
3.15
Problem: Dirac-delta Potentials in Two Dimensions
34
3.16
Problem: Graphene
35
3.17
Problem: Effective Mass
35
3.18
Problem: Cyclotron Frequency
35
3.19
Problem:
de Haas-van Alphen
35
3.20
Problem: Fermi Energy
36
4
Density of States
37
4.1
Problem: Density of States
39
4.2
Problem: Two-dimensional Density of States
40
4.3
Problem: Two-dimensional Tight Binding
40
4.4
Problem: Tight Binding from One to Three Dimensions
40
4.5
Problem: Crossover to Quasi-one-dimensional Metal
41
4.6
Problem: Phonon Mode of Two-dimensional System
42
4.7
Problem: Saddle Point
42
4.8
Problem: Density of States in Superconductors
43
4.9
Problem: Energy Gap
43
Contents
VII
4.10 Problem:
Density of States for Hybridized Bands
43
4.11
Problem: Infinite-dimensional DOS
44
4.12
Problem: Two-to Three-dimensional Crossover
44
4.13
Problem: One-to Two-dimensional Crossover
45
4.14
Problem: Carbon Nanotube
45
5
Elementary Excitations
47
5.1
Problem: Tight-binding Model
50
5.2
Problem: Impurity State in the One-dimensional Tight-binding
Model
51
5.3
Problem: Hybridization of Energy Bands
51
5.4
Problem:
Polarons
52
5.5
Problem: Polaritons
52
5.6
Problem:
Excitons
52
5.7
Problem:
Holstein-PrimakofF
Transformation
53
5.8
Problem: Dyson-Maleev Representation
53
5.9
Problem: Spin Waves
53
5.10
Problem: Spin Waves Again
54
5.11
Problem:
Anisotropie Heisenberg
Model
54
5.12
Problem:
Solitons 54
5.13
Problem: Dirac
Fermions
in Graphene
56
6
Thermodynamics of Noninteracting Quasiparticles
57
6.1
Problem: Specific Heat of Metals and Insulators
64
6.2
Problem: Number of Phonons
64
6.3
Problem: Energy of the Phonon Gas
64
6.4
Problem: Bulk Modulus of the Phonon Gas
64
6.5
Problem: Phonons in One Dimension
64
6.6
Problem: Electron-Hole Symmetry
65
6.7
Problem: Entropy of the Noninteracting Electron Gas
65
6.8
Problem: Free Energy with Gap at the Fermi Energy
65
6.9
Problem: Bulk Modulus at
Γ
= 0 66
6.10
Problem: Temperature Dependence of the Bulk Modulus
66
6.11
Problem: Chemical Potential of the Free-electron Gas
66
6.12
Problem: EuO Specific Heat
66
6.13
Problem: Magnetization at Low Temperatures
66
6.14
Problem: Electronic Specific Heat
66
6.15
Problem: Quantum Hall Effect
67
7
Transport Properties
69
7.1
Problem: Temperature-dependent Resistance
76
7.2
Problem: Conductivity Tensor
76
7.3
Problem: Montgomery' Method
76
7.4
Problem:
Anisotropie
Layer
77
7.5
Problem: Two-charge-carrier
Drude
Model
78
VIII Contents
7.6
Problem:
Thermal
Conductivity
78
7.7
Problem: Residual Resistivity
78
7.8
Problem: Electric and Heat Transport
79
7.9
Problem: Conductivity of Tight-binding Band
79
7.10
Problem: Hall Effect in Two-dimensional Metals
80
7.11
Problem: Free-electron Results from the Boltzmann Equations
80
7.12
Problem:
p
-п
Junctions
80
7.13
Problem: Mott-Ioffe-Regel
81
8
Optical Properties
83
8.1
Problem: Reflectivity and Transmission: Multiple Interfaces
93
8.2
Problem: Group Velocity
93
8.3
Problem: Tinkham Formula
94
8.4
Problem: Transmission of a Thin Superconductor
94
8.5
Problem: Fourier Transform Infrared Spectroscopy
95
8.6
Problem: Sum Rule: Dielectric Constant
96
8.7
Problem: Optical Mode of KBr
96
8.8
Problem: Direct-gap Semiconductor
96
8.9
Problem: Inversion Symmetry
97
8.10
Problem: Frequency-dependent Conductivity
97
8.11
Problem: Frequency-dependent Response of a Superconductor
97
8.12
Problem: Optical Conductivity Tensor
98
8.13
Problem: Joint Density of States in One Dimension
98
8.14
Problem: One-dimensional Semiconductor
98
8.15
Problem: Conductivity of Graphene
99
8.16
Problem:
Biodi
Oscillations
99
9
Interactions and Phase Transitions
101
9.1
Problem: Spontaneous Polarization
205
9.2
Problem: Divergent Susceptibility
206
9.3
Problem: Large-U Hubbard Model
106
9.4
Problem: Infinite-range Hubbard Model
207
9.5
Problem:
Stoner
Model
107
9.6
Problem: One-dimensional Electron System
107
9.7
Problem: Peierls Distortion 20S
9.8
Problem: Singularity at 2kF
208
9.9
Problem: Susceptibility of a One-dimensional Electron Gas
209
9.10
Problem: Critical Temperature in Mean Field Approximation
209
9.11
Problem: Instability of Half-filled Band
209
9.12
Problem: Screening of an Impurity Charge
220
9.13
Problem: Fermi Surface Nesting in Two Dimensions
220
9.14
Problem: Fermi Surface Nesting in Quasi-one-dimension 111
9.15
Problem: Anderson Model
222
9.16
Problem: Collective Jahn-Teller Distortion
113
Contents
IX
ΊΟ
Mesoscopic and Nanoscale Systems 115
10.1 Problem: Differential
Conductance of
a
Tunnel
Junction
122
10.2 Problem: Sharvin
Formula
122
10.3 Problem:
Ballistic
Transport 123
10.4 Problem:
Tunneling from a Ballistic Conductor
123
10.5
Problem: Reflectivity of a Lattice Defect
124
10.6
Problem: Two Scatterers: Incoherent Propagation
125
10.7
Problem: Two Scatterers: Coherent Propagation
125
10.8
Problem: Strong Localization
126
10.9
Problem: Coulomb Blockade
126
10.10
Problem: Single-atom Transistor
127
Partii
Solutions to Problems
129
Π
Crystal Structures
131
11.1
Solution: Symmetries
131
11.2
Solution: Rotations
131
11.3
Solution: Copper Oxide Layers
132
11.4
Solution: Graphite
133
11.5
Solution: Structure of
АуСбо
133
11.6
Solution: hep
andate
Structures
134
11.7
Solution: hep and bee Structures
135
11.8
Solution: Structure Factor of AxC60
136
11.9
Solution: Neutron Diffraction Device
337
11.10
Solution: Linear Array of Emitters, Finite Size Effects
137
11.11
Solution: Linear Array of Emitters:
Superlattice 139
11.12
Solution: Powder Diffraction of hep and fee Crystals
140
11.13
Solution: Momentum Resolution
342
11.14
Solution: Finite Size Effects
143
11.15
Solution: Random Displacement
245
11.16
Hint: Vacancies
346
11.17
Hint: Integrated Scattering Intensity
246
12
Interatomic Forces and Lattice Vibrations
247
12.1
Solution: Madelung Constant
247
12.2
Solution: NaCl Bulk Modulus
149
12.3
Hint: Madelung with Screened Potential
252
12.4
Solution: Triple-axis Spectrometer
252
12.5
Solution: Phonons in Silicon
252
12.6
Solution: Linear Array of Emitters: Phonons
252
12.7
Hint: Long-range Interaction
252
12.8
Solution: Mass Defect
153
12.9
Solution: Debye Frequency
254
12.10
Solution: Vibrations of a Square Lattice
155
12.11
Solution:
Grüneisen
Parameter
256
Χ Ι
Contents
12.12
Solution: Diatomic Chain
157
12.13
Hint: Damped Oscillation
159
12.14
Solution: Two-dimensional Debye
159
12.15
Solution: Soft Optical Phonons
160
12.16
Hint: Soft Phonons Again
162
12.17
Solution: Nanowire Phonons
162
13
Electronic Band Structure
163
13.1
Solution: Nearly Free Electrons in One Dimension
163
13.2
Solution: Eigenfunctions of Nearly Free Electrons in One
Dimension
164
13.3
Solution: Tight-binding Hamiltonian
366
13.4
Solution: Nearly Free Electrons in Dirac-delta Potentials
166
13.5
Solution: Tight binding in Dirac-delta Potentials
166
13.6
Solution: Dirac-delta Potentials
168
13.7
Solution: Band Overlap
171
13.8
Solution: Nearly Free Electrons in Two Dimensions
172
13.9
Solution: Nearly Free-electron Bands
174
13.10
Solution: Instability at the Fermi Wavenumber
174
13.11
Solution: Electrons in 2D Nearly Free-electron Band
176
13.12
Solution: Square Lattice
178
13.13
Solution: Tight-binding Band in Two Dimensions
179
13.14
Solution: Electrons in 2D Tight-binding Band
180
13.15
Solution: Dirac-delta Potentials in Two Dimensions
181
13.16
Hint: Graphene
181
13.17
Hint: Effective Mass
182
13.18
Hint: Cyclotron Frequency
184
13.19
Solution:
de Haas-van Alphen
184
13.20
Hint: Fermi Energy
184
14
Density of States
187
14.1
Solution: Density of States
187
14.2
Solution: Two-dimensional Density of States
187
14.3
Solution: Two-dimensional Tight-binding
188
14.4
Solution: Tight-binding from One to Three Dimensions
189
14.5
Solution: Crossover to Quasi-one-dimensional Metal
191
14.6
Solution: Phonon Mode of Two-dimensional System
193
14.7
Solution: Saddle Point
194
14.8
Solution: Density of States in Superconductors
196
14.9
Solution: Energy Gap
397
14.10
Solution: Density of States for Hybridized Bands
197
14.11
Solution: Infinite-dimensional DOS
199
14.12
Solution: Two- to Three-dimensional Crossover
200
14.13
Solution: One-to Two-dimensional Crossover
201
14.14
Solution: Carbon Nanotube
202
Contents
XI
15
Elementary
Excitations
205
15.1
Solution:
Tight-binding Model
203
15.2
Solution:
Impurity
State
in the One-dimensional Tight-binding
Model
205
15.3
Solution: Hybridization of Energy Bands
206
15.4
Solution:
Polarons
208
15.5
Solution: Polaritons
210
15.6
Hint:
Excitons
211
15.7
Solution: Holstein-PrimakofFTransformation
212
15.8
Hint: Dyson-Maleev Representation
212
15.9
Solutions: Spin Waves
212
15.10
Solution: Spin Waves Again
214
15.11
Solution:
Anisotropie Heisenberg
Model
214
15.12
Hint:
Solitons 215
15.13
Solution: Dirac
Fermions
in Graphene
216
16
Thermodynamics of Noninteracting Quasiparticles
217
16.1
Solution: Specific Heat of Metals and Insulators
217
16.2
Solution: Number of Phonons
227
16.3
Solution: Energy of the Phonon Gas
238
16.4
Solution: Bulk Modulus of the Phonon Gas
220
16.5
Hint: Phonons in One Dimension
221
16.6
Solution: Electron-Hole Symmetry
221
16.7
Solution: Entropy of the Noninteracting Electron Gas
223
16.8
Solution: Free Energy with Gap at the Fermi Energy
224
16.9
Solution: Bulk Modulus at
Γ
= 0 226
16.10
Solution: Temperature Dependence of the Bulk Modulus
226
16.11
Solution: Chemical Potential of the Free-electron Gas
227
16.12
Solution: EuO Specific Heat
229
16.13
Hint: Magnetization at Low Temperatures
230
16.14
Solution: Electronic Specific Heat
230
16.15
Solution: Quantum Hall Effect
232
17
Transport Properties
235
17.1
Solution: Temperature-dependent Resistance
235
17.2
Solution: Conductivity Tensor
236
17.3
Solution: Montgomery Method
238
17.4
Solution:
Anisotropie
Layer
238
17.5
Solution: Two-charge-carrier
Drude
Model
240
17.6
Solution: Thermal Conductivity
242
17.7
Hint: Residual Resistivity
243
17.8
Solution: Electric and Heat Transport
243
17.9
Solution: Conductivity of Tight-binding Band
244
XII Contents
17.10
Solution: Hall
Effect in Two-dimensional Metals
246
17.11
Solution: Free-electron Results from the Boltzmann Equations
248
17.12
Solution:
p
-п
Junctions
250
17.13
Solution: Mott-Ioffe-Regel
251
18
Optical Properties
253
18.1
Solution: Reflectivity and Transmission: Multiple Interfaces
253
18.2
Solution: Group Velocity
254
18.3
Solution: Tinkham Formula
255
18.4
Solution: Transmission of a Thin Superconductor
256
18.5
Solution: Fourier Transform Infrared Spectroscopy
257
18.6
Solution: Sum Rule: Dielectric Constant
257
18.7
Solution: Optical Mode of KBr
257
18.8
Solution: Direct-gap Semiconductor
258
18.9
Solution: Inversion Symmetry
259
18.10
Solution: Frequency-dependent Conductivity
260
18.11
Solution: Frequency-dependent Response of a Superconductor
263
18.12
Solution: Optical Conductivity Tensor
264
18.13
Solution: Joint Density of States in One Dimension
265
18.14
Solution: One-dimensional Semiconductor
266
18.15
Solution: Conductivity of Graphene
268
18.16
Solution: Bloch Oscillations
269
19
Interactions and Phase Transitions
273
19.1
Solution: Spontaneous Polarization
273
19.2
Solution: Divergent Susceptibility
274
19.3
Solution: Large-U Hubbard Model
275
19.4
Solution: Infinite-range Hubbard Model
278
19.5
Hint:
Stoner
Model
279
19.6
Solution: One-dimensional Electron System
279
19.7
Solution: Peierls Distortion
281
19.8
Solution: Singularity at 2fcF
282
19.9
Solution: Susceptibility of a One-dimensional Electron Gas
283
19.10
Solution: Critical Temperature in Mean Field Approximation
284
19.11
Solution: Instability of Half-filled Band
284
19.12
Solution: Screening of an Impurity Charge
285
19.13
Solution: Fermi Surface Nesting in Two Dimensions
287
19.14
Solution: Fermi Surface Nesting in Quasi One Dimension
288
19.15
Solution: Anderson Model
291
19.16
Solution: Collective Jahn-Teller Distortion
294
20
Mesoscopic and
Nano-scale
Systems
297
20.1
Solution: Differential Conductance of a Tunnel Junction
297
20.2
Solution: Sharvin Formula
297
20.3
Solution: Ballistic Transport
298
Contents
XIII
20.4
Solution: Tunneling from a Ballistic Conductor
299
20.5
Solution: Reflectivity of a Lattice Defect
299
20.6
Solution: Two Scatterers: Incoherent Propagation
300
20.7
Solution: Two Scatterers: Coherent Propagation
301
20.8
Solution: Strong Localization
301
20.9
Solution: Coulomb Blockade
302
20.10
Solution: Single-atom Transistor
303
References
305
Index
307 |
| any_adam_object | 1 |
| 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. |
| author_role | aut aut |
| author_sort | Mihály, László 1949- |
| author_variant | l m lm m c m mc mcm |
| building | Verbundindex |
| bvnumber | BV035002693 |
| callnumber-first | Q - Science |
| callnumber-label | QC176 |
| callnumber-raw | QC176.515 |
| callnumber-search | QC176.515 |
| callnumber-sort | QC 3176.515 |
| callnumber-subject | QC - Physics |
| classification_rvk | UP 1050 |
| classification_tum | PHY 601f PHY 003f |
| ctrlnum | (OCoLC)299239702 (DE-599)DNB988812509 |
| dewey-full | 530.41 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.41 |
| dewey-search | 530.41 |
| dewey-sort | 3530.41 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2., rev. and enl. ed. |
| format | Book |
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| genre_facet | Aufgabensammlung |
| id | DE-604.BV035002693 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:41:01Z |
| indexdate | 2024-07-20T09:47:31Z |
| institution | BVB |
| isbn | 9783527408559 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016672068 |
| oclc_num | 299239702 |
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| physical | XVIII, 315 S. graph. Darst. |
| publishDate | 2009 |
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| record_format | marc |
| series2 | Physics textbook |
| spelling | Mihály, László 1949- Verfasser (DE-588)13669411X aut Solid state physics problems and solutions Laszlo Mihaly ; Michael C. Martin 2., rev. and enl. ed. Weinheim WILEY-VCH 2009 XVIII, 315 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics textbook Solid state physics Solid state physics Problems, exercises, etc 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 http://d-nb.info/988812509/04 Inhaltsverzeichnis text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3112974&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=016672068&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 Solid state physics Solid state physics Problems, exercises, etc 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 Laszlo Mihaly ; Michael C. Martin |
| title_fullStr | Solid state physics problems and solutions Laszlo Mihaly ; Michael C. Martin |
| title_full_unstemmed | Solid state physics problems and solutions Laszlo Mihaly ; Michael C. Martin |
| title_short | Solid state physics |
| title_sort | solid state physics problems and solutions |
| title_sub | problems and solutions |
| topic | Solid state physics Solid state physics Problems, exercises, etc Festkörperphysik (DE-588)4016921-2 gnd |
| topic_facet | Solid state physics Solid state physics Problems, exercises, etc Festkörperphysik Aufgabensammlung |
| url | http://d-nb.info/988812509/04 http://deposit.dnb.de/cgi-bin/dokserv?id=3112974&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=016672068&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mihalylaszlo solidstatephysicsproblemsandsolutions AT martinmichaelc solidstatephysicsproblemsandsolutions |
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