Group theory in physics: 1
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Academic Press
(1984)
|
| Schriftenreihe: | Techniques of physics
7,1 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 371, XXVIII S. |
| ISBN: | 0121898032 |
Internformat
MARC
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| 100 | 1 | |a Cornwell, J. F. |d 1937- |e Verfasser |0 (DE-588)1054411123 |4 aut | |
| 245 | 1 | 0 | |a Group theory in physics |n 1 |c J. F. Cornwell |
| 264 | 1 | |a London [u.a.] |b Academic Press |c (1984) | |
| 300 | |a XVI, 371, XXVIII S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Techniques of physics |v 7,1 | |
| 490 | 0 | |a Techniques of Physics |v ... | |
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Datensatz im Suchindex
| _version_ | 1804116824646746112 |
|---|---|
| adam_text | Contents
Preface
Contents
of
Volume
II
XIII
PART A FUNDAMENTAL
CONCEPTS
1
The Basic Framework
1
The concept
of a group
2
Groups of coordinate transformations
(a) Rotations
(b) Translations
3
The group of the
Schrödinger
equation
(a) The Hamiltonian operator
(b) The
invariance
of the Hamiltonian operator
(c) The scalar transformation operators P(T)
4
The role of matrix representations
3
7
7
12
13
13
14
16
19
2
The Structure of Groups
1
Some elementary considerations
2
Classes
3
Invariant subgroups
4
Cosets
5
Factor groups
6
Homomorphic and isomorphic mappings
7
Direct product groups and semi-direct product groups
ix
23
23
25
27
28
31
33
37
χ
CONTENTS
3
Lie Groups
44
1
Definition of a linear Lie group
44
2
The connected components of a linear Lie group
52
3
Compact and non-compact linear Lie groups
56
4
Invariant integration
58
5
The homomorphic mapping of SU(2) onto S0{3)
63
6
The homomorphic mapping of the group SL{2, C) onto the
proper orthochronous
Lorentz
group L+
65
4
Representations of Groups
—
Principal Ideas
68
1
Definitions
68
2
Equivalent representations
71
3
Unitary representations
73
4
Reducible and irreducible representations
77
5
Schur s Lemmas and the orthogonality theorem for matrix
representations
80
6
Characters
83
7
Methods for finding the irreducible representations of the
physically important groups
89
(a) Finite groups
89
(b) Lie groups
90
5
Representations of Groups
—
Developments
92
1
Projection operators
92
2
Direct product representations
98
3
The Wigner-Eckert Theorem for groups of coordinate
transformations in R3
101
4
The Wigner-Eckart Theorem generalized
109
5
Representations of direct product groups
113
6
Irreducible representations of finite Abelian groups
117
7
Induced representations
П8
8
The reality of representations
127
6
Group Theory in Quantum Mechanical Calculations
130
1
The solution of the Schrodinger equation
130
2
Transition probabilities and selection rules
134
3
Time-indepenrient perturbation theory
138
4
Generalization of the theory to incorporate spin- particles
142
(a) The spinor transformation operators
142
(b) Double groups
147
(c) The spinor Hamiltonian operator
149
(d) Spinor basis functions and energy eigenfunctions
151
(e) Irreducible representations of double groups
153
(f) Splitting of degeneracies by spin-orbit coupling
156
5
Time-reversal symmetry
158
(a) Spin-independent theory
158
(b) Spin-dependent theory
159
CONTENTS xi
PART
В
APPLICATIONS IN MOLECULAR AND SOLID STATE
PHYSICS
163
7
The Group Theoretical Treatment of
Vîbratîonal
Problems
165
1
Introduction
165
2
Generat
theory of vibrations
166
(a) Classical theory
166
(b) Quantum theory
169
3
Symmetry considerations
170
(a) Motivation
170
(b) The
invariance
group
172
<c) The displacement representation
175
(d) Partial diagonalization of the force matrix
F
179
{e)
Analysis in terms of basis vectors
183
(ƒ)
Extra degeneracies caused by the reality of
F
187
(g)
Symmetry coordinates
189
(h) Zero-frequency modes of molecules
190
8
The Translational Symmetry of Crystalline Solids
198
1
The
Bravais
lattices
198
2
The cyclic boundary conditions
202
(a) Electronic wave functions
202
(b) Lattice vibrations
204
3
The irreducible representations of the group
2Г
of pure
primitive translations and Bloch s Theorem
207
4
Brillouin zones
209
5
Electronic energy bands
214
6
Irreducible representations of the double group 9~° of pure
primitive translations
217
7
Lattice vibrations
218
9
The
Cristallographie
Space Groups
1
A survey of the crystallographic space groups
222
2
Irreducible representations of symmorphic space groups
226
(a) The fundamental theorem on irreducible representations of
symmorphic space groups
226
(b) The irreducible representations of the cubic space groups
О1*,
OČ
and O*
231
3
Irreducible representations of non-symmorphjc space groups
235
(a) The fundamental theorem on the irreducible
representations of non-symmorphic space groups
235
(b) The relevant irreducible representations of ^(k)
239
(c) The irreducible representations of the space group Oh of
the diamond structure
242
4
Consequences of the fundamental theorems
245
(a) Degeneracies of eigenvalues and the symmetry of e(k) and
245
xii CONTENTS
(b)
Continuity and compatibility of the irreducible
representations of %>(k) and ^(k)
248
(c) Origin and orientation dependence of the symmetry
labelling of electronic and lattice vibrational states
251
5
Irreducible representations of double space groups
253
6
Selection rules
255
APPENDICES
259
Appendix A Matrices
261
1
Definitions
261
2
Eigenvalues and eigenvectors
265
Appendix
В
Vector Spaces
270
1
The concept of a vector space
270
2
Inner product spaces
274
3
Hubert spaces
278
4
Linear operators
280
5
Bilinear forms
284
6
Linear functionals
286
7
Direct product spaces
288
8
Quaternions
291
Appendix
С
Proofs of Certain Theorems on Group Representations
294
1
Proofs of Theorems I and IV of Chapter
4,
Section
3 294
2
Proof of lemma required for Theorem I of Chapter
4,
Section
4 298
3
Proofs of Theorems I and IV of Chapter
4,
Section
5 299
4
Proofs of Theorems IV,
VII,
VIII
and IX of Chapter
4,
Section
6 302
5
Proof of theorems of Chapter
5,
Section
1 307
6
Proof of the Wigner-Eckart Theorem, Theorem II of Chapter
5,
Section
3 310
7
Proof of Theorem II of Chapter
5,
Section
5 311
8
Proofs of the theorems of Chapter
5,
Section
7 312
9
Proofs of Theorems II, III and IV of Chapter
5,
Section
8 319
Appendix
D
Character Tables of Point Groups
323
1
The single crystallography point groups
323
2
The double crystallographic point groups
342
3
The linear infinite point groups Dxh and C^
355
References
357
Index
|
| any_adam_object | 1 |
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| indexdate | 2024-07-09T15:44:39Z |
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| isbn | 0121898032 |
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| spelling | Cornwell, J. F. 1937- Verfasser (DE-588)1054411123 aut Group theory in physics 1 J. F. Cornwell London [u.a.] Academic Press (1984) XVI, 371, XXVIII S. txt rdacontent n rdamedia nc rdacarrier Techniques of physics 7,1 Techniques of Physics ... (DE-604)BV002365698 1 Techniques of physics 7,1 (DE-604)BV001890126 7,1 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001557700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cornwell, J. F. 1937- Group theory in physics Techniques of physics |
| title | Group theory in physics |
| title_auth | Group theory in physics |
| title_exact_search | Group theory in physics |
| title_full | Group theory in physics 1 J. F. Cornwell |
| title_fullStr | Group theory in physics 1 J. F. Cornwell |
| title_full_unstemmed | Group theory in physics 1 J. F. Cornwell |
| title_short | Group theory in physics |
| title_sort | group theory in physics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001557700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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