9-j Symbol - Orthogonality Relation

Orthogonality Relation

The 9-j symbols satisfy this orthogonality relation:

\sum_{j_7 j_8} (2j_7+1)(2j_8+1) \begin{Bmatrix} j_1 & j_2 & j_3\\ j_4 & j_5 & j_6\\ j_7 & j_8 & j_9 \end{Bmatrix} \begin{Bmatrix} j_1 & j_2 & j_3'\\ j_4 & j_5 & j_6'\\ j_7 & j_8 & j_9 \end{Bmatrix} = \frac{\delta_{j_3j_3'}\delta_{j_6j_6'} \{j_1j_2j_3\} \{j_4j_5j_6\} \{j_3j_6j_9\}} {(2j_3+1)(2j_6+1)}.

The symbol (called the triangular delta) is equal to one if the triad satisfies the triangular conditions and zero otherwise.

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