Clebsch gordon coefficients are used in a change of basis/representation .

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