Difference between revisions of "Cg fast.m"
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==Syntax== | ==Syntax== | ||
| − | cg=cg_fast(L,M,L1,M1,L2,M2) | + | cg=cg_fast(L,M,L1,M1,L2,M2) |
==Arguments== | ==Arguments== | ||
| − | L,M,L1,M1,L2,M2 - integer or half-integer indices of | + | L,M,L1,M1,L2,M2 - integer or half-integer indices of |
the angular momentum or spin states | the angular momentum or spin states | ||
==Outputs== | ==Outputs== | ||
| − | cg - floating-point (double precision) | + | cg - floating-point (double precision) |
Clebsch-Gordan coefficient | Clebsch-Gordan coefficient | ||
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==Notes== | ==Notes== | ||
Revision as of 17:37, 5 June 2026
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
Notes
- 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.
- 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
