Difference between revisions of "Cg fast.m"
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{{DISPLAYTITLE:cg_fast.m}} __NOTOC__ | {{DISPLAYTITLE:cg_fast.m}} __NOTOC__ | ||
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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. | 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== | ==Syntax== | ||
| − | + | cg=cg_fast(L,M,L1,M1,L2,M2) | |
==Arguments== | ==Arguments== | ||
| − | + | 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) | |
| − | + | 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. | ||
| + | |||
| + | ilya.kuprov@weizmann.ac.il | ||
==Notes== | ==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. | # 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. | # 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== | ==See also== | ||
| + | |||
[[clebsch_gordan.m]], [[wigner.m]], [[wigner_3j.m]], [[wigner_6j.m]] | [[clebsch_gordan.m]], [[wigner.m]], [[wigner_3j.m]], [[wigner_6j.m]] | ||
Revision as of 15:01, 5 April 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
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.
ilya.kuprov@weizmann.ac.il
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
