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ClebschGordan

Clebsch-Gordan coefficients matrices (SymPy, WMA)

ClebschGordan[{$j_1$, $m_1$}, {$j_2$, $m_2$}, {j m}]

returns the Clebsch-Gordan coefficient for the decomposition of $|j, m\rangle$ in terms of $|j_1, m\rangle$, $|j_2, m2\rangle$.

• • ClebschGordan[{3 / 2, 3 / 2}, {1 / 2, -1 / 2}, {1, 1}]

ClebschGordan works with integer and half‐integer arguments:

• • ClebschGordan[{1/2, -1/2}, {1/2, -1/2}, {1, -1}]

• • ClebschGordan[{1/2, -1/2}, {1, 0}, {1/2, -1/2}]

Compare with WMA example:

• • ClebschGordan[{5, 0}, {4, 0}, {1, 0}] == Sqrt[5 / 33]