This is a table of ClebschâÂÂGordan coefficients used for adding angular momentum values in quantum mechanics. The overall sign of the coefficients for each set of constant , , is arbitrary to some degree and has been fixed according to the CondonâÂÂShortley and Wigner sign convention as discussed by Baird and Biedenharn. Tables with the same sign convention may be found in the Particle Data Group's Review of Particle Properties and in online tables.
The ClebschâÂÂGordan coefficients are the solutions to
Explicitly:
The summation is extended over all integer for which the argument of every factorial is nonnegative.
For brevity, solutions with and are omitted. They may be calculated using the simple relations
and
The ClebschâÂÂGordan coefficients for j values less than or equal to 5/2 are given below.
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When , the ClebschâÂÂGordan coefficients are given by .
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Algorithms to produce ClebschâÂÂGordan coefficients for higher values of and , or for the su(N) algebra instead of su(2), are known. A web interface for tabulating SU(N) ClebschâÂÂGordan coefficients is readily available.