Contents
1
Operations ................................
1
1 . 1 O p e r a t i o n sa n dP o i n t s ........................
1
1.2 Operations and Functions . . . ...................
4
1 . 3 O p e r a t i o n sa n dO p e r a t o r s ......................
8
1 . 4 A nA i d eM é m o i r e .......................... 10
1 . 5 P r o b l e m s............................... 10
References ................................. 10
2
Function Spaces and Matrices ...................... 11
2.1 Function Spaces ........................... 11
2.2 Linear Operators and Transformation Matrices . . ......... 12
2 . 3 U n i t a r yM a t r i c e s........................... 14
2.4 Time Reversal as an Anti-linear Operator .............. 16
2 . 5 P r o b l e m s............................... 19
References ................................. 19
3
Groups ................................... 21
3 . 1 T h eS y m m e t r yo fA m m o n i a..................... 21
3 . 2 T h eG r o u pS t r u c t u r e......................... 24
3.3 Some Special Groups ........................ 27
3.4 Subgroups . ............................. 29
3 . 5 C o s e t s ................................ 30
3 . 6 C l a s s e s................................ 32
3.7 Overview of the Point Groups . ................... 34
Spherical Symmetry and the Platonic Solids . . . ......... 34
C y l i n d r i c a lS y m m e t r i e s ....................... 40
3.8 Rotational Groups and Chiral Molecules .............. 44
3.9 Applications: Magnetic and Electric Fields ............. 46
3 . 1 0P r o b l e m s............................... 47
References ................................. 48
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