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BUILT-IN MATHEMATICA SYMBOL

ThreeJSymbol

gives the values of the Wigner 3-

symbol.

The parameters of ThreeJSymbol can be integers, half-integers or symbolic expressions.

The Clebsch-Gordan coefficients and 3- symbols in Mathematica satisfy the relation .

Use symbolic arguments to obtain exact symbolic answers:

Out[1]=

Use symbolic arguments to obtain exact symbolic answers:

Out[1]=

ThreeJSymbol works with integer and half-integer arguments:

Plot 3-

symbol coefficients as a function of

and

Apply angular momentum operators to spherical harmonics:

Evaluate Gaunt coefficients:

Evaluate an explicit triple integral of spherical harmonics:

Evaluate the completely symbolic case of ThreeJSymbol:

Demonstrate

-sum orthogonality:

Convert to a Regge R symbol:

Check the symmetry of the Regge R symbol:

Compare with sum definition:

A message is issued and the result 0 returned in the case