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)

Arguments

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

Note: only some combinations of L,M,L1,M1,L2,M2 are allowed by the pro-
      perties of spherical harmonics and spin states. If inadmissible
      indices are supplied, zero is returned.

Note: CG coefficient calculation in double-precision arithmetic is not
      a trivial matter for high ranks. This function produces fast ans-
      wers 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.

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