Group theory and quantum mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, NY
Dover Publ.
2003
|
| Edition: | 1. publ., unabridged republ. of the work originally publ. ... in 1964 |
| Series: | Dover books on chemistry
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 340 S. graph. Darst. |
| ISBN: | 0486432475 9780486432472 |
Staff View
MARC
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| 100 | 1 | |a Tinkham, Michael |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Group theory and quantum mechanics |c Michael Tinkham |
| 250 | |a 1. publ., unabridged republ. of the work originally publ. ... in 1964 | ||
| 264 | 1 | |a Mineola, NY |b Dover Publ. |c 2003 | |
| 300 | |a XII, 340 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Dover books on chemistry | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Quantum theory | |
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Record in the Search Index
| _version_ | 1804133406352605184 |
|---|---|
| adam_text | CONTENTS
Preface V
1 Introduction I
1-1
The Nature of the Problem
/
1-2
The Role of Symmetry
3
2
Abstract Group Theory
6
2-1
Definitions and Nomenclature
6
2-2
Illustrative Examples
7
2-3
Rearrangement Theorem
8
2-4
Cyclic Groups
9
2-5
Subgroups and Coscts
У
2-6
Ľxample
Groups of Finite Order
W
2-7
Conjugate Elements and Class Structure
12
2-8
Normal Divisors and Factor Groups
13
2-9
Class Multiplication
15
Exercises
16
References
17
3
Theory of Group Representations
18
3-1
Definitions
ÍS
3-2
Proof of the Orthogonality Theorem
20
3-3
The Character of a Representation
25
χ
CONTENTS
3-4
Construction
of Character Tables
28
3-5
Decomposition of Reducible Representations
29
3-6
Application of Representation Theory in Quantum Mechanics
31
3-7
Illustrative Representations of Abelian Groups
37
3-8
Basis Functions for Irreducible Representations
39
3-9
Direct-product Groups
43
3-10
Direct-product Representations within a Group
46
Exercises
47
References
48
4
Physical Applications of Group Theory SO
4-1
Crystal-symmetry Operators
51
4-2
The Crystallographic Point Groups
54
4-3
Irreducible Representations of the Point Groups
62
A
-А
Elementary Representations of the Three-dimensional Rotation Group
65
4-5
Crystal-field Splitting of Atomic Energy Levels
67
4-6
Intermediate Crystal-field-splitting Case
69
4-7
Weak-crystal-field Case and Crystal Double Groups
75
4-8
Introduction of Spin Effects in the Medium-field Case
78
4-9
Group-theoretical Matrix-element Theorems
80
4-Ю
Selection Rules and Parity
82
4-11
Directed Valence
87
4-12
Application of Group Theory to Directed Valence
89
Exercises
92
References
93
5
Full Rotation Group and Angular Momentum
94
5-1
Rotational Transformation Properties and Angular Momentum
94
5-2
Continuous Groups
98
5-3
Representation of Rotations through Eulerian Angles
101
5-4
Homomorphism with the Unitary Group
103
5-5
Representations of the Unitary Group
106
5-6
Representation of the Rotation Group by Representations
of the Unitary Group
109
5-7
Application of the Rotation-representation Matrices 111
5-8
Vector Model for Addition of Angular Momenta
115
5-9
The Wigner or Clebsch-Gordan Coefficients
117
5-10
Notation, Tabulations, and Symmetry Properties
of the Wigner Coefficients
121
5-11
Tensor Operators
124
CONTENTS xi
5-12
The Wigner-Eckart Theorem
131
5-13
The Racah Coefficients
133
5-14
Application of Racah Coefficients
137
5-15
The Rotation-Inversion Group
139
5-16
Time-reversal Symmetry
141
5-17
More General
Invariances
147
Exercises
151
References
153
6
Quantum Mechanics of Atoms
/54
6-1
Review of Elementary Atomic Structure and Nomenclature
155
6-2
The Hamiltonian
157
6-3
Approximate Eigenfunctions
157
6-4
Calculation of Matrix Elements between Determinantal
Wavefunctions
162
6-5
Hartree-Fock Method
167
6-6
Calculation of L-S-term Energies
170
6-7
Evaluation of Matrix Elements of the Energy
173
6-8
Eigenfunctions and Angular-momentum Operations
178
6-9
Calculation of Fine Structure
181
6-10
Zeeman
Effect
188
6-11
Magnetic Hyperfine Structure
193
6-12
Electric Hyperfine Structure
201
Exercises
206
References
208
7
Molecular Quantum Mechanics
210
7-1
Bom-Oppenheimer Approximation
210
7-2
Simple Electronic Eigenfunctions
213
7-3
Irreducible Representations for Linear Molecules
216
7-4
The Hydrogen Molecule
219
7-5
Molecular
Orbitals 220
7-6
Heitler-London Method
223
7-7
Orthogonal Atomic
Orbitals 226
7-8
Group Theory and Molecular
Orbitals 227
7-9
Selection Rules for Electronic Transitions
233
7-10
Vibration of Diatomic Molecules
234
7-11
Normal Modes in Polyatomic Molecules
238
7-12
Group Theory and Normal Modes
242
7-13
Selection Rules for Vibrational Transitions
248
xii CONTENTS
7-14
Molecular
Rotation 250
7-15
Effect of Nuclear Statistics on Molecular Rotation
252
7-16
Asymmetric Rotor
255
7-17
Vibration-Rotation Interaction
257
7-18
Rotation-Electronic Coupling
260
Exercises
264
References
266
8
Solid-state Theory
267
8-1
Symmetry Properties in Solids
267
8-2
The Reciprocal Lattice and Brillouin Zones
270
8-3
Form of Energy-band Wavefunctions
275
8-4
Crystal Symmetry and the Group of the
k
Vector
279
8-5
Pictorial Consideration of Eigenfunctions
281
8-6
Formal Consideration of Degeneracy and Compatibility
284
8-7
Group Theory and the Plane-wave Approximation
290
8-8
Connection between Tight- and Loose-binding Approximations
293
8-9
Spin-orbit Coupling in Band Theory
295
8-10
Time Reversal in Band Theory
297
8-11
Magnetic Crystal Groups
299
8-12
Symmetries of Magnetic Structures
303
8-13
The Landau Theory of Second-order Phase Transitions
309
8-14
Irreducible Representations of Magnetic Groups
311
Exercises
313
References
315
Appendix
A Review of Vectors, Vector Spaces, and Matrices
317
В
Character Tables for Point-symmetry Groups
323
С
Tables of ck and
cř
Coefficients for s, p, and
d
Electrons
331
Index
335
|
| any_adam_object | 1 |
| author | Tinkham, Michael |
| author_facet | Tinkham, Michael |
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| discipline | Chemie / Pharmazie Physik |
| edition | 1. publ., unabridged republ. of the work originally publ. ... in 1964 |
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| indexdate | 2024-07-09T20:08:12Z |
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| isbn | 0486432475 9780486432472 |
| language | English |
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| physical | XII, 340 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Dover Publ. |
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| series2 | Dover books on chemistry |
| spelling | Tinkham, Michael Verfasser aut Group theory and quantum mechanics Michael Tinkham 1. publ., unabridged republ. of the work originally publ. ... in 1964 Mineola, NY Dover Publ. 2003 XII, 340 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dover books on chemistry Quantentheorie Group theory Quantum theory Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Gruppentheorie (DE-588)4072157-7 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013202328&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tinkham, Michael Group theory and quantum mechanics Quantentheorie Group theory Quantum theory Quantenmechanik (DE-588)4047989-4 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4072157-7 |
| title | Group theory and quantum mechanics |
| title_auth | Group theory and quantum mechanics |
| title_exact_search | Group theory and quantum mechanics |
| title_full | Group theory and quantum mechanics Michael Tinkham |
| title_fullStr | Group theory and quantum mechanics Michael Tinkham |
| title_full_unstemmed | Group theory and quantum mechanics Michael Tinkham |
| title_short | Group theory and quantum mechanics |
| title_sort | group theory and quantum mechanics |
| topic | Quantentheorie Group theory Quantum theory Quantenmechanik (DE-588)4047989-4 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Quantentheorie Group theory Quantum theory Quantenmechanik Gruppentheorie |
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