Symmetry principles in solid state and molecular physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola
Dover Publ.
2001
|
| Edition: | unabridged republication of the orig. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 499 S. Ill., graph. Darst. |
| ISBN: | 0486420019 9780486420011 |
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MARC
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| 100 | 1 | |a Lax, Melvin J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Symmetry principles in solid state and molecular physics |c Melvin Lax |
| 250 | |a unabridged republication of the orig. ed. | ||
| 264 | 1 | |a Mineola |b Dover Publ. |c 2001 | |
| 300 | |a XI, 499 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Física do estado sólido |2 larpcal | |
| 650 | 7 | |a Simetria (física de partículas) |2 larpcal | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Lattice theory | |
| 650 | 4 | |a Molecules | |
| 650 | 4 | |a Solid state physics | |
| 650 | 4 | |a Symmetry (Physics) | |
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| 650 | 0 | 7 | |a Festkörperphysik |0 (DE-588)4016921-2 |2 gnd |9 rswk-swf |
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| _version_ | 1804137916361867264 |
|---|---|
| adam_text | CONTENTS
Chapter
1.
Relation
of
Group
Theory to Quantum Mechanics
... 1
1.1.
Symmetry Operations
.......... 2
1.2.
Abstract Group Theory
......... 6
1.3.
Commuting
Observables
and Classes
..... 9
1.4.
Representations and Irreducible
Representations
........... 13
1.5.
Relation between Representations,
Characters, and States
.......... 19
1.6.
Continuous Groups
........... 25
1.7.
Summary
.............. 29
Chapter
2.
Point Groups
................ 34
2.1.
Generators of the Proper Rotation
Group
R
+(3)
............. 35
2.2.
The Commutator Algebra of
R +(3)
..... 37
2.3.
Irreducible Representations of
R
(З) .
. . . .38
2.4.
Characters of the Irreducible
Representations of
R
+(3)
........ 39
2.5.
The Three-Dimensional Representation
j=lofÄ+(3)
............ 40
2.6.
The Spin Representation^
{
of
R
(З)
.... 43
2.7.
Class Structure of Point Groups
....... 47
2.8.
The Proper Point Groups
......... 49
2.9.
Nature of Improper Rotations in a
Finite Group
............. 51
2.10.
Relation between Improper and Proper Groups
. 54
2.1
L
Representations of Groups Containing
the Inversion
............. 55
2.12.
Product Groups
............ 56
vii
viii Contents
2.13.
Representations of an Outer
Product Group
. . 57
2.14.
Enumeration of the Improper Point Groups
. . 58
2.15.
Crystallographic Point Groups
....... 61
2.16.
Double Point Groups
.......... 62
2.17.
Summary
.............. 64
Chapter
3.
Point Group Examples
.............69
3.1.
Electric and Magnetic Dipoles: Irreducible
Components of a Reducible Space
......69
3.2.
Crystal Field Theory without Spin:
Compatibility Relations
.........73
3.3.
Product Representations and Decomposition
of Angular Momentum
..........77
3.4.
Selection Rules
............82
3.5.
Spin and Spin-Orbit Coupling
.......89
3.6.
Crystal Field Theory with Spin
.......93
3.7.
Projection Operators
..........99
3.8.
Crystal Harmonics
...........101
3.9.
Summary
..............105
Chapter
4.
Macroscopic Crystal Tensors
...........
Ill
4.1.
Macroscopic Point Group Symmetry
.....
Ill
4.2.
Tensors of the First Rank: Ferroelectrics
and Ferromagnetics
...........112
4.3.
Second-Rank Tensors: Conductivity,
Susceptibility
.............114
4.4.
Direct Inspection Methods for Tensors
of Higher Rank: the Hall Effect
......118
4.5.
Method of Invariants
..........120
4.6.
Measures of Infinitesimal and Finite Strain
. . . 124
4.7.
The Elasticity Tensor for Group C3v
.....129
4.8.
Summary
..............130
Chapter
5.
Molecular Vibrations
.............134
5.1.
Representations Contained in NH3 Vibrations
. .135
5.2.
Determination of the Symmetry Vectors
forNH3
...............139
5.3.
Symmetry Coordinates, Normal Coordinates,
Internal Coordinates, and Invariants
.....146
5.4.
Potential Energy and Force Constants
. . . .153
5.5.
The Number of Force Constants
......161
Contents
ix
5.6.
Summary
..............165
Chapter
6.
Translational Properties of Crystals
........169
6.1.
Crystal Systems,
Bravais
Lattices, and
Crystal Classes
.............169
6.2.
Representations of the Translation Group
. . . .181
6.3.
Reciprocal Lattices and Brillouin Zones
. . . .185
6.4.
Character Orthonormality Theorems
.....186
6.5.
Conservation of Crystal Momentum
.....188
6.6.
Laue-Bragg X-ray Diffraction
........189
6.7.
Summary
...............192
Chapter
7.
Electronic Energy Bands
............194
7.1.
Relation between the Many-Electron and
One-Electron Viewpoints
.........195
7.2.
Concept of an Energy Band
........198
7.3.
The Empty Lattice
...........199
7.4.
Almost-Free Electrons
..........201
7.5.
Energy Gaps and Symmetry Considerations
. . . 204
7.6.
Points of Zero Slope
...........206
7.7.
Periodicity in Reciprocal Space
.......208
7.8.
The
к
·
ρ
Method of Analytical Continuation
. .211
7.9.
Dynamics of Electron Motion in Crystals
. . . 220
7.10.
Effective Hamiltonians and Donor States
. . .224
7.11.
Summary
...............227
Chapter
8.
Space Groups
................231
8.1.
Screw Axes and Glide Planes
........231
8.2.
Restrictions on Space Group Elements
.....232
8.3.
Equivalence of Space Groups
........235
8.4.
Construction of Space Groups
.......236
8.5.
Factor Groups of Space Groups
.......238
8.6.
Group Gk of the Wave Vector
к
.......240
8.7.
Space Group Algebra
..........243
8.8.
Representations of Symmorphic Space Groups
. . 244
8.9.
Representations of Nonsymmorphic
Space Groups
.............244
8.10.
Class Structure and Algebraic Treatment
of Multiplier Groups
...........247
8.11.
Double Space Groups
..........250
8.12.
Summary
...............252
χ
Contents
Chapter
9.
Space Group Examples
............256
9.1.
Vanishing Electric Moment in Diamond
. . . .256
9.2.
Induced Quadrupole Moments in Diamond
. . . 260
9.3.
Force Constants in Crystals
........261
9.4.
Local Electric Moments
..........264
9.5.
Symmetries of Acoustic and Optical Modes
of Vibration
..............267
9.6.
Hole Scattering by Phonons
........270
9.7.
Selection Rules for Direct Optical Absorption
. .271
9.8.
Summary
...............273
Chapter
10.
Time Reversal
...............275
10.1.
Nature of Time-Reversal Operators
without Spin
.............275
10.2.
Time Reversal with Spin
.........277
10.3.
Time Reversal in External Fields
......280
10.4. Antilinear
and Antiunitary Operators
.....281
10.5.
Onsager Relations
...........287
10.6.
The Time-Reversed Representation
.....292
10.7.
Time-Reversal Degeneracies
........301
10.8.
The Herring Criterion for Space Groups
. . . .305
10.9.
Selection Rules Due to Time Reversal
. . . .312
10.10.
Summary
..............319
Chapter
11.
Lattice Vibration Spectra
............324
11.1.
Inelastic Neutron Scattering
........324
11.2.
Transformation to Normal Coordinates
.... 326
11.3.
Quantized Lattice Oscillators: Phonons
. . . .331
11.4.
Crystal Momentum
...........333
11.5.
Infinitesimal Displacement and Rotational
Invariance
..............335
11.6.
Symmetry Properties of the Dynamical Matrix
. . 336
11.7.
Consequences of Time Reversal
.......340
11.8.
Form and Number of Independent Constants
in the Dynamical Matrix for Internal and
Zone Boundary Points
..........344
11.9.
The Method of Long Waves: Primitive Lattices
.346
11.10.
Nonprimitive
Lattices and Internal Shifts
. . .350
11.11.
Summary
..............357
Contents
xi
Chapter
12.
Vibrations of Lattices with the Diamond Structure
. . . 363
12.1.
Force Constants and the Dynamical Matrix
. .363
12.2.
Symmetry of
Vibrationsat
Δ
= {q,
0,0) . . . .366
12.3.
R (q)
and w(q) for
q = (q,
0,0)........374
12.4.
Σ
Modes (q,q,0)
............377
12.5.
TheModesA = (9,ç,9)andL = (24r/a)(ii^)
.382
12.6.
Elastic Properties of the Diamond Structure
. . 385
12.7.
Comparison with Experiment
.......387
12.8.
Summary
..............388
Chapter
13.
Symmetry of Molecular Wave Functions
.......390
13.1.
Molecular Orbital Theory
.........390
13.2.
Valence Bond
Orbitals..........393
13.3.
Many-Body Wave Functions and
Chemical Structures
...........404
13.4.
Hartree-Fock Wave Functions and Broken
Symmetry
..............409
13.5.
The Jahn-Teller Effect
..........413
13.6.
Summary
..............414
Appendix A. Character Tables and Basis Functions for the
Single and Double Point Groups
.........416
Appendix B. Schoenflies, International, and Herring Notations
. . . 433
Appendix C. Decomposition of D/ of Full Rotation Group
into Point Group Representations
.........436
Appendix D. Orthogonality Properties of Eigenvectors
of the Equation
ΑΨ^λΒ-φ;
Reciprocals
of Singular Matrices
.............439
Appendix E. The BriHouin Zones
.............443
Appendix F. Multiplier Representations for the Point Groups
.... 452
Appendix G. Wigner Mappings and the Fundamental Theorem
of
Projective
Geometry
............461
Appendix H. Generalized Mobility Theory
..........466
Author Index and Bibliography
..............469
Subject Index
....................481
Symbol Index
....................491
|
| adam_txt |
CONTENTS
Chapter
1.
Relation
of
Group
Theory to Quantum Mechanics
. 1
1.1.
Symmetry Operations
. 2
1.2.
Abstract Group Theory
. 6
1.3.
Commuting
Observables
and Classes
. 9
1.4.
Representations and Irreducible
Representations
. 13
1.5.
Relation between Representations,
Characters, and States
. 19
1.6.
Continuous Groups
. 25
1.7.
Summary
. 29
Chapter
2.
Point Groups
. 34
2.1.
Generators of the Proper Rotation
Group
R
+(3)
. 35
2.2.
The Commutator Algebra of
R +(3)
. 37
2.3.
Irreducible Representations of
R
"'"(З) .
. . . .38
2.4.
Characters of the Irreducible
Representations of
R
+(3)
. 39
2.5.
The Three-Dimensional Representation
j=lofÄ+(3)
. 40
2.6.
The Spin Representation^
{
of
R
"""(З)
. 43
2.7.
Class Structure of Point Groups
. 47
2.8.
The Proper Point Groups
. 49
2.9.
Nature of Improper Rotations in a
Finite Group
. 51
2.10.
Relation between Improper and Proper Groups
. 54
2.1
L
Representations of Groups Containing
the Inversion
. 55
2.12.
Product Groups
. 56
vii
viii Contents
2.13.
Representations of an Outer
Product Group
. . 57
2.14.
Enumeration of the Improper Point Groups
. . 58
2.15.
Crystallographic Point Groups
. 61
2.16.
Double Point Groups
. 62
2.17.
Summary
. 64
Chapter
3.
Point Group Examples
.69
3.1.
Electric and Magnetic Dipoles: Irreducible
Components of a Reducible Space
.69
3.2.
Crystal Field Theory without Spin:
Compatibility Relations
.73
3.3.
Product Representations and Decomposition
of Angular Momentum
.77
3.4.
Selection Rules
.82
3.5.
Spin and Spin-Orbit Coupling
.89
3.6.
Crystal Field Theory with Spin
.93
3.7.
Projection Operators
.99
3.8.
Crystal Harmonics
.101
3.9.
Summary
.105
Chapter
4.
Macroscopic Crystal Tensors
.
Ill
4.1.
Macroscopic Point Group Symmetry
.
Ill
4.2.
Tensors of the First Rank: Ferroelectrics
and Ferromagnetics
.112
4.3.
Second-Rank Tensors: Conductivity,
Susceptibility
.114
4.4.
Direct Inspection Methods for Tensors
of Higher Rank: the Hall Effect
.118
4.5.
Method of Invariants
.120
4.6.
Measures of Infinitesimal and Finite Strain
. . . 124
4.7.
The Elasticity Tensor for Group C3v
.129
4.8.
Summary
.130
Chapter
5.
Molecular Vibrations
.134
5.1.
Representations Contained in NH3 Vibrations
. .135
5.2.
Determination of the Symmetry Vectors
forNH3
.139
5.3.
Symmetry Coordinates, Normal Coordinates,
Internal Coordinates, and Invariants
.146
5.4.
Potential Energy and Force Constants
. . . .153
5.5.
The Number of Force Constants
.161
Contents
ix
5.6.
Summary
.165
Chapter
6.
Translational Properties of Crystals
.169
6.1.
Crystal Systems,
Bravais
Lattices, and
Crystal Classes
.169
6.2.
Representations of the Translation Group
. . . .181
6.3.
Reciprocal Lattices and Brillouin Zones
. . . .185
6.4.
Character Orthonormality Theorems
.186
6.5.
Conservation of Crystal Momentum
.188
6.6.
Laue-Bragg X-ray Diffraction
.189
6.7.
Summary
.192
Chapter
7.
Electronic Energy Bands
.194
7.1.
Relation between the Many-Electron and
One-Electron Viewpoints
.195
7.2.
Concept of an Energy Band
.198
7.3.
The Empty Lattice
.199
7.4.
Almost-Free Electrons
.201
7.5.
Energy Gaps and Symmetry Considerations
. . . 204
7.6.
Points of Zero Slope
.206
7.7.
Periodicity in Reciprocal Space
.208
7.8.
The
к
·
ρ
Method of Analytical Continuation
. .211
7.9.
Dynamics of Electron Motion in Crystals
. . . 220
7.10.
Effective Hamiltonians and Donor States
. . .224
7.11.
Summary
.227
Chapter
8.
Space Groups
.231
8.1.
Screw Axes and Glide Planes
.231
8.2.
Restrictions on Space Group Elements
.232
8.3.
Equivalence of Space Groups
.235
8.4.
Construction of Space Groups
.236
8.5.
Factor Groups of Space Groups
.238
8.6.
Group Gk of the Wave Vector
к
.240
8.7.
Space Group Algebra
.243
8.8.
Representations of Symmorphic Space Groups
. . 244
8.9.
Representations of Nonsymmorphic
Space Groups
.244
8.10.
Class Structure and Algebraic Treatment
of Multiplier Groups
.247
8.11.
Double Space Groups
.250
8.12.
Summary
.252
χ
Contents
Chapter
9.
Space Group Examples
.256
9.1.
Vanishing Electric Moment in Diamond
. . . .256
9.2.
Induced Quadrupole Moments in Diamond
. . . 260
9.3.
Force Constants in Crystals
.261
9.4.
Local Electric Moments
.264
9.5.
Symmetries of Acoustic and Optical Modes
of Vibration
.267
9.6.
Hole Scattering by Phonons
.270
9.7.
Selection Rules for Direct Optical Absorption
. .271
9.8.
Summary
.273
Chapter
10.
Time Reversal
.275
10.1.
Nature of Time-Reversal Operators
without Spin
.275
10.2.
Time Reversal with Spin
.277
10.3.
Time Reversal in External Fields
.280
10.4. Antilinear
and Antiunitary Operators
.281
10.5.
Onsager Relations
.287
10.6.
The Time-Reversed Representation
.292
10.7.
Time-Reversal Degeneracies
.301
10.8.
The Herring Criterion for Space Groups
. . . .305
10.9.
Selection Rules Due to Time Reversal
. . . .312
10.10.
Summary
.319
Chapter
11.
Lattice Vibration Spectra
.324
11.1.
Inelastic Neutron Scattering
.324
11.2.
Transformation to Normal Coordinates
. 326
11.3.
Quantized Lattice Oscillators: Phonons
. . . .331
11.4.
Crystal Momentum
.333
11.5.
Infinitesimal Displacement and Rotational
Invariance
.335
11.6.
Symmetry Properties of the Dynamical Matrix
. . 336
11.7.
Consequences of Time Reversal
.340
11.8.
Form and Number of Independent Constants
in the Dynamical Matrix for Internal and
Zone Boundary Points
.344
11.9.
The Method of Long Waves: Primitive Lattices
.346
11.10.
Nonprimitive
Lattices and Internal Shifts
. . .350
11.11.
Summary
.357
Contents
xi
Chapter
12.
Vibrations of Lattices with the Diamond Structure
. . . 363
12.1.
Force Constants and the Dynamical Matrix
. .363
12.2.
Symmetry of
Vibrationsat
Δ
= {q,
0,0) . . . .366
12.3.
R (q)
and w(q) for
q = (q,
0,0).374
12.4.
Σ
Modes (q,q,0)
.377
12.5.
TheModesA = (9,ç,9)andL = (24r/a)(ii^)
.382
12.6.
Elastic Properties of the Diamond Structure
. . 385
12.7.
Comparison with Experiment
.387
12.8.
Summary
.388
Chapter
13.
Symmetry of Molecular Wave Functions
.390
13.1.
Molecular Orbital Theory
.390
13.2.
Valence Bond
Orbitals.393
13.3.
Many-Body Wave Functions and
Chemical Structures
.404
13.4.
Hartree-Fock Wave Functions and Broken
Symmetry
.409
13.5.
The Jahn-Teller Effect
.413
13.6.
Summary
.414
Appendix A. Character Tables and Basis Functions for the
Single and Double Point Groups
.416
Appendix B. Schoenflies, International, and Herring Notations
. . . 433
Appendix C. Decomposition of D/ of Full Rotation Group
into Point Group Representations
.436
Appendix D. Orthogonality Properties of Eigenvectors
of the Equation
ΑΨ^λΒ-φ;
Reciprocals
of Singular Matrices
.439
Appendix E. The BriHouin Zones
.443
Appendix F. Multiplier Representations for the Point Groups
. 452
Appendix G. Wigner Mappings and the Fundamental Theorem
of
Projective
Geometry
.461
Appendix H. Generalized Mobility Theory
.466
Author Index and Bibliography
.469
Subject Index
.481
Symbol Index
.491 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Lax, Melvin J. |
| author_facet | Lax, Melvin J. |
| author_role | aut |
| author_sort | Lax, Melvin J. |
| author_variant | m j l mj mjl |
| building | Verbundindex |
| bvnumber | BV035000289 |
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| callnumber-search | QC174.5 |
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| callnumber-subject | QC - Physics |
| classification_rvk | UP 1200 |
| ctrlnum | (OCoLC)46808543 (DE-599)BVBBV035000289 |
| dewey-full | 530.4/1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.4/1 |
| dewey-search | 530.4/1 |
| dewey-sort | 3530.4 11 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | unabridged republication of the orig. ed. |
| format | Book |
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| id | DE-604.BV035000289 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:40:12Z |
| indexdate | 2024-07-09T21:19:54Z |
| institution | BVB |
| isbn | 0486420019 9780486420011 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016669698 |
| oclc_num | 46808543 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-634 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-634 DE-188 |
| physical | XI, 499 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Dover Publ. |
| record_format | marc |
| spelling | Lax, Melvin J. Verfasser aut Symmetry principles in solid state and molecular physics Melvin Lax unabridged republication of the orig. ed. Mineola Dover Publ. 2001 XI, 499 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Física do estado sólido larpcal Simetria (física de partículas) larpcal Group theory Lattice theory Molecules Solid state physics Symmetry (Physics) Symmetrie (DE-588)4058724-1 gnd rswk-swf Molekülphysik (DE-588)4039979-5 gnd rswk-swf Molekül (DE-588)4039972-2 gnd rswk-swf Molekülsymmetrie (DE-588)4170385-6 gnd rswk-swf Festkörper (DE-588)4016918-2 gnd rswk-swf Festkörperphysik (DE-588)4016921-2 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Molekül (DE-588)4039972-2 s Gruppentheorie (DE-588)4072157-7 s DE-604 Festkörperphysik (DE-588)4016921-2 s Festkörper (DE-588)4016918-2 s Symmetrie (DE-588)4058724-1 s Molekülsymmetrie (DE-588)4170385-6 s Molekülphysik (DE-588)4039979-5 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016669698&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lax, Melvin J. Symmetry principles in solid state and molecular physics Física do estado sólido larpcal Simetria (física de partículas) larpcal Group theory Lattice theory Molecules Solid state physics Symmetry (Physics) Symmetrie (DE-588)4058724-1 gnd Molekülphysik (DE-588)4039979-5 gnd Molekül (DE-588)4039972-2 gnd Molekülsymmetrie (DE-588)4170385-6 gnd Festkörper (DE-588)4016918-2 gnd Festkörperphysik (DE-588)4016921-2 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4058724-1 (DE-588)4039979-5 (DE-588)4039972-2 (DE-588)4170385-6 (DE-588)4016918-2 (DE-588)4016921-2 (DE-588)4072157-7 |
| title | Symmetry principles in solid state and molecular physics |
| title_auth | Symmetry principles in solid state and molecular physics |
| title_exact_search | Symmetry principles in solid state and molecular physics |
| title_exact_search_txtP | Symmetry principles in solid state and molecular physics |
| title_full | Symmetry principles in solid state and molecular physics Melvin Lax |
| title_fullStr | Symmetry principles in solid state and molecular physics Melvin Lax |
| title_full_unstemmed | Symmetry principles in solid state and molecular physics Melvin Lax |
| title_short | Symmetry principles in solid state and molecular physics |
| title_sort | symmetry principles in solid state and molecular physics |
| topic | Física do estado sólido larpcal Simetria (física de partículas) larpcal Group theory Lattice theory Molecules Solid state physics Symmetry (Physics) Symmetrie (DE-588)4058724-1 gnd Molekülphysik (DE-588)4039979-5 gnd Molekül (DE-588)4039972-2 gnd Molekülsymmetrie (DE-588)4170385-6 gnd Festkörper (DE-588)4016918-2 gnd Festkörperphysik (DE-588)4016921-2 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Física do estado sólido Simetria (física de partículas) Group theory Lattice theory Molecules Solid state physics Symmetry (Physics) Symmetrie Molekülphysik Molekül Molekülsymmetrie Festkörper Festkörperphysik Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016669698&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT laxmelvinj symmetryprinciplesinsolidstateandmolecularphysics |