Introduction to group theory with applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Acad. Press
1977
|
| Schriftenreihe: | Materials science and technology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 429 S. |
| ISBN: | 0121457508 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to group theory with applications |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Preface xiii
Acknowledgments xv
Chapter 1 Symmetry Operations
1 1 Introduction 1
1 2 Point Symmetry Operations 2
1 3 The Stereographic Projection 8
1 4 The 32 Crystallographic Point Groups 10
1 5 Related Considerations 13
1 6 Space Group Example 16
Notes 18
Problems 19
Chapter 2 Group Concepts
2 1 Introduction 21
2 2 Definition of a Group 21
2 3 Symmetry Operations Form a Group 25
2 4 Related Group Concepts 25
2 5 Isomorphism and Homomorphism 27
2 6 Special Kinds of Groups 28
2 7 More Involved Group Concepts (including a Factor
Group of a Space Group) 30
Appendix to Chapter 2 32
Notes 35
Problems 35
vii
Chapter 3 Matrix Representations of Finite Groups
3 1 Introduction 37
3 2 Representations 38
3 3 Irreducible Representations 41
3 4 Representations of a Factor Group 45
Appendix to Chapter 3 46
Notes 47
Problems 48
Chapter 4 Characters of Matrix Representations of Finite Groups
4 1 Properties of Characters of Irreducible
Representations 50
4 2 Character Tables 57
4 3 Reduction of a Reducible Representation 59
4 4 Basis Functions 60
4 5 Examples—Neumann Principle 63
4 6 Atomic Positions 70
4 7 The Hamiltonian 72
Appendix to Chapter 4 74
Notes 75
Problems 75
Chapter 5 Vibrations of Molecules and Crystals
5 1 3N Degrees of Freedom 79
5 2 General Considerations 80
5 3 Number and Type of Normal Modes for Molecules 84
5 4 Internal Coordinates 89
5 5 Crystals 90
5 6 Eigenvectors and Symmetry Adapted Vectors 94
5 7 Projection Operators 96
5 8 Projection Operators Applied to Normal
Coordinates 98
Notes 102
Problems 103
Chapter 6 Normal Modes (Direct Product and Selection Rules)
6 1 Direct Product of Irreducible Representations 105
6 2 Vibrational Wave Function 110
6 3 Selection Rules—Infrared and Raman 112
6 4 Molecular Approximations (Site Symmetry and
Davydov Splitting) 120
Notes 122
Problems 123
Chapter 7 Quantum Mechanics
7 1 Atomic Wave Functions 125
7 2 Transformation of Functions 127
7 3 Eigenfunctions as Basis Functions 131
7 4 Proper Rotations and Angular Momentum 135
7 5 Perturbations 137
7 6 Matrix Elements (Selection Rules) 141
7 7 General Secular Equation Problem 148
Appendix to Chapter 7 151
Notes 153
Problems 154
Chapter 8 Crystal Field Theory (and Atomic Physics)
8 1 Rotations in Terms of Euler Angles 157
8 2 Representations of the Full Rotation Group 159
8 3 Reduction of Symmetry 162
8 4 Energy Level Diagrams (Correlation Diagrams) 167
8 5 Crystal Double Groups 179
8 6 Correlation Diagrams including Double Groups 184
8 7 Other Crystal Field Effects 187
Appendix to Chapter 8 190
Notes 196
Problems 197
Chapter 9 Hybrid Functions
9 1 Introduction 199
9 2 Simple Hybrid Functions and Bonding 201
9 3 Tetrahedral Hybridization 202
9 4 Other Hybrid Functions 206
9 5 ir Hybrid Functions 208
9 6 Comment on Hybrid Orbitals (Slater Determinant) 213
Notes 214
Problems 215
Chapter 10 Molecular Orbital Theory
10 1 Hydrogen Molecular Ion 216
10 2 Simple MO Theory 219
10 3 Transition Metal Complexes 220
10 4 LCAO MO of ir Electrons in Conjugated
Hydrocarbons 232
10 5 Woodward Hoffman Rules 239
Notes 246
Problems 247
Chapter 11 Symmetry of Crystal Lattices
11 1 The Real Affine Group 250
11 2 Space Group 251
11 3 Translational Lattice 254
11 4 International Tables for X Ray Crystallography,
International Notation, etc. 264
11 5 Magnetic Groups (Color Groups) 274
Notes 280
Problems 281
Chapter 12 Band Theory of Solids
12 1 Translational Symmetry 284
12 2 Symmorphic Space Groups 300
12 3 Nonsymmorphic Space Groups 321
12 4 Spin Orbit Effects on Bands 326
12 5 Time Reversal Symmetry 332
Notes 339
Problems 339
Chapter 13 The Full Rotation Group
13 1 The Homomorphism between the Special Unitary
Group in Two Dimensions, SU(2), and the Three
Dimension Rotation Group 341
13 2 Irreducible Representations of SU(2) 345
13 3 Wigner Coefficients 347
13 4 Irreducible Tensor Operators 351
13 5 The Wigner Eckart Theorem 355
13 6 Survey of 3j and Racah Coefficients 364
Notes 366
Problems 367
Appendix 1 Crystal Systems 371
Appendix 2 The 32 Point Groups 377
Appendix 3 Character Tables 379
Appendix 4 Space Groups 391
Appendix 5 Matrices, Vector Spaces, and Linear Operators 396
Appendix 6 Direct Product Tables 403
Appendix 7 Correlation Tables 405
Appendix 8 Spherical Harmonics 409
Appendix 9 Tanable Sugano Diagrams 413
Appendix 10 Double Group Character Tables 417
Bibliography 420
Index 425
|
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| indexdate | 2024-07-09T15:42:47Z |
| institution | BVB |
| isbn | 0121457508 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001478959 |
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| physical | XV, 429 S. |
| publishDate | 1977 |
| publishDateSearch | 1977 |
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| series2 | Materials science and technology |
| spelling | Burns, Gerald Verfasser aut Introduction to group theory with applications New York Acad. Press 1977 XV, 429 S. txt rdacontent n rdamedia nc rdacarrier Materials science and technology Groupes, Théorie des Group theory Anwendung (DE-588)4196864-5 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Anwendung (DE-588)4196864-5 s DE-604 Physik (DE-588)4045956-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001478959&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burns, Gerald Introduction to group theory with applications Groupes, Théorie des Group theory Anwendung (DE-588)4196864-5 gnd Physik (DE-588)4045956-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4045956-1 (DE-588)4072157-7 |
| title | Introduction to group theory with applications |
| title_auth | Introduction to group theory with applications |
| title_exact_search | Introduction to group theory with applications |
| title_full | Introduction to group theory with applications |
| title_fullStr | Introduction to group theory with applications |
| title_full_unstemmed | Introduction to group theory with applications |
| title_short | Introduction to group theory with applications |
| title_sort | introduction to group theory with applications |
| topic | Groupes, Théorie des Group theory Anwendung (DE-588)4196864-5 gnd Physik (DE-588)4045956-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Groupes, Théorie des Group theory Anwendung Physik Gruppentheorie |
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