properties for

- basis independent
- choose phase s.t.
- (selection rule)
- completeness
- orthogonality
- symmetry
- Usually defined by recursion relations

example: angular momentum coupling.

where the last braket is a clebsch-gordon coefficient. Nonzero clebsch-gordon
coefficient if . Define # of states with fixed with . Define
# of 2j+1-plets with . Note that . This means if , if , and
if . This means if or 0 otherwise. In general, . Recursion
relations:

source

psfile jl@crush.caltech.edu index

angular_momentum_coupling

wigner_eckhart_theorem