cg_fast.m

Clebsch-Gordan coefficient: the coefficient in front of Y(L,M) spherical harmonic in the expansion of the product of Y(L1,M1) and Y(L2,M2) spherical harmonics. In the more general sense, the coefficient refers to the expansion coefficient of |L,M> angular momentum or spin state in the product basis of |L1,M1>|L2,M2> states.

Syntax

    cg=cg_fast(L,M,L1,M1,L2,M2)

Parameters

    L,M,L1,M1,L2,M2  - integer or half-integer indices of 
                       the angular momentum or spin states

Outputs

    cg               - floating-point (double precision)
                       Clebsch-Gordan coefficient

Notes

1. Only some combinations of L,M,L1,M1,L2,M2 are allowed by the properties of spherical harmonics and spin states. If inadmissible indices are supplied, zero is returned.
2. CG coefficient calculation in double-precision arithmetic is not a trivial matter for high ranks. This function produces fast answers with an accuracy of about 1e-3 up to about L=20. A slower machine precision implementation for higher ranks is available in clebsch_gordan.m function.

See also

clebsch_gordan.m, wigner.m, wigner_3j.m, wigner_6j.m

SU(2), SO(3), and other groups

Version 2.8, authors: Ilya Kuprov