clebsch_gordan.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=clebsch_gordan(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

Examples

>> format long
>> clebsch_gordan(9500,-9000,5600,-4800,6400,-4200)

ans =

   0.012291987779716

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 machine precision answers up to about L=1e4. A faster implementation for low ranks is available in cg_fast.m function.

See also

cg_fast.m, wigner.m, wigner_3j.m, wigner_6j.m, add_spins.m, comm.m, hilb2liouv.m, irr_sph_ten.m, ist_product_table.m, lorentz.m, mat2sphten.m, multipack.m, pauli.m, perm_group.m, rocomm.m, rwalk.m, sle_operators.m, sorensen.m, spher_harmon.m, sphten2mat.m, stev2sph.m, stevens.m, superop.m, twospinist.m, Kernel_utilities

Version 2.8, authors: Ilya Kuprov