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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Combinatorial Functions >

Built-in Mathematica Symbol

ClebschGordan

ClebschGordan[{j₁, m₁}, {j₂, m₂}, {j, m}]
gives 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:

Use symbolic arguments to obtain exact symbolic answers:

ClebschGordan works with integer and half-integer arguments:

For symbolic input ClebschGordan evaluates to ThreeJSymbol:

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