This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# ClebschGordan

 ClebschGordangives the Clebsch-Gordan coefficient for the decomposition of in terms of .
• The Clebsch-Gordan coefficients vanish except when and the satisfy a triangle inequality.
• The parameters of ClebschGordan can be integers, half-integers, or symbolic expressions.
• Mathematica uses the standard conventions of Edmonds for the phase of the Clebsch-Gordan coefficients.
Use symbolic arguments to obtain exact symbolic answers:
 Out[1]=

Use symbolic arguments to obtain exact symbolic answers:
 Out[1]=
 Scope   (2)
ClebschGordan works with integer and half-integer arguments:
For symbolic input ClebschGordan evaluates to ThreeJSymbol:
 Applications   (3)
Plot Clebsch-Gordan coefficients as a function of and :
Decompose a spherical harmonic into a sum of products of two spherical harmonics:
Apply angular momentum operators to spherical harmonics:
Evaluate the completely symbolic case of ClebschGordan:
Demonstrate -sum orthogonality:
A message is issued and the result of 0 is returned when :
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