Contents
xiii
7 . 4 T h eC o u p l i n go fS p i n s........................173
7.5 Double Groups ............................175
7.6 Kramers Degeneracy .........................180
T i m e - R e v e r s a lS e l e c t i o nR u l e s ...................182
7.7 Application: Spin Hamiltonian for the Octahedral Quartet State . . 184
7 . 8 P r o b l e m s...............................189
References .................................190
Appendix A Character Tables ........................191
A.1 Finite Point Groups .........................192
C 1 and the Binary Groups C s ,C i ,C 2 ................192
The Cyclic Groups C n (n = 3, 4, 5, 6, 7, 8 ) .............192
The Dihedral Groups D n (n = 2, 3, 4, 5, 6 ) .............194
The Conical Groups C nv (n = 2, 3, 4, 5, 6 ) .............195
The C nh Groups (n = 2, 3, 4, 5, 6 )..................196
The Rotation–Reflection Groups S 2n (n = 2, 3, 4 ) .........197
The Prismatic Groups D nh (n = 2, 3, 4, 5, 6, 8 )...........198
The Antiprismatic Groups D nd (n = 2, 3, 4, 5, 6 )..........199
The Tetrahedral and Cubic Groups .................201
The Icosahedral Groups .......................202
A.2 Infinite Groups ............................203
C y l i n d r i c a lS y m m e t r y........................203
Spherical Symmetry .........................204
Appendix B Symmetry Breaking by Uniform Linear Electric
and Magnetic Fields ...........................205
B.1 Spherical Groups ...........................205
B.2 Binary and Cylindrical Groups ...................205
Appendix C Subduction and Induction ..................207
C.1 Subduction G ↓ H ..........................207
C.2 Induction: H ↑ G ..........................211
Appendix D Canonical-Basis Relationships ................215
Appendix E Direct-Product Tables .....................219
Appendix F Coupling Coefficients .....................221
Appendix G Spinor Representations ....................235
G . 1 C h a r a c t e rT a b l e s...........................235
G.2 Subduction . .............................237
G.3 Canonical-Basis Relationships ...................237
G.4 Direct-Product Tables ........................240
G . 5 C o u p l i n gC o e f fi c i e n t s ........................241
Solutions to Problems .............................245
References ...................................261
Index ......................................263
xiii
7 . 4 T h eC o u p l i n go fS p i n s........................173
7.5 Double Groups ............................175
7.6 Kramers Degeneracy .........................180
T i m e - R e v e r s a lS e l e c t i o nR u l e s ...................182
7.7 Application: Spin Hamiltonian for the Octahedral Quartet State . . 184
7 . 8 P r o b l e m s...............................189
References .................................190
Appendix A Character Tables ........................191
A.1 Finite Point Groups .........................192
C 1 and the Binary Groups C s ,C i ,C 2 ................192
The Cyclic Groups C n (n = 3, 4, 5, 6, 7, 8 ) .............192
The Dihedral Groups D n (n = 2, 3, 4, 5, 6 ) .............194
The Conical Groups C nv (n = 2, 3, 4, 5, 6 ) .............195
The C nh Groups (n = 2, 3, 4, 5, 6 )..................196
The Rotation–Reflection Groups S 2n (n = 2, 3, 4 ) .........197
The Prismatic Groups D nh (n = 2, 3, 4, 5, 6, 8 )...........198
The Antiprismatic Groups D nd (n = 2, 3, 4, 5, 6 )..........199
The Tetrahedral and Cubic Groups .................201
The Icosahedral Groups .......................202
A.2 Infinite Groups ............................203
C y l i n d r i c a lS y m m e t r y........................203
Spherical Symmetry .........................204
Appendix B Symmetry Breaking by Uniform Linear Electric
and Magnetic Fields ...........................205
B.1 Spherical Groups ...........................205
B.2 Binary and Cylindrical Groups ...................205
Appendix C Subduction and Induction ..................207
C.1 Subduction G ↓ H ..........................207
C.2 Induction: H ↑ G ..........................211
Appendix D Canonical-Basis Relationships ................215
Appendix E Direct-Product Tables .....................219
Appendix F Coupling Coefficients .....................221
Appendix G Spinor Representations ....................235
G . 1 C h a r a c t e rT a b l e s...........................235
G.2 Subduction . .............................237
G.3 Canonical-Basis Relationships ...................237
G.4 Direct-Product Tables ........................240
G . 5 C o u p l i n gC o e f fi c i e n t s ........................241
Solutions to Problems .............................245
References ...................................261
Index ......................................263