• ← SixJSymbol

ThreeJSymbol

3-j symbol (SymPy, WMA)

ThreeJSymbol[{$j_1$, $m_1$}, {$j_2$, $m_2$}, {$j_3$, $m_3$}]

returns the values of the Wigner 3-j symbol.

Compare with SymPy examples:

• • ThreeJSymbol[{2, 0}, {6, 0}, {4, 0}]

ThreeJSymbol is symmetric under permutations:

• • % == ThreeJSymbol[{2, 0}, {4, 0}, {6, 0}] == ThreeJSymbol[{4, 0}, {2, 0}, {6, 0}]

• • ThreeJSymbol[{2, 0}, {6, 0}, {4, 1}]

Compare with WMA examples:

• • ThreeJSymbol[{6, 0}, {4, 0}, {2, 0}] == Sqrt[5 / 143]

• • ThreeJSymbol[{2, 1}, {2, 2}, {4, -3}] == -(1 / (3 Sqrt[2]))

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

Result 0 returned for unphysical cases:

• • ThreeJSymbol[{1, 2}, {3, 4}, {5, 12}]

Arguments must be integer or half integer values:

• • ThreeJSymbol[{2.1, 6}, {4, 0}, {0, 0}]