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.

Read more about this topic:  9-j Symbol

Famous quotes containing the word relation:

    “It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
    —René Descartes (1596–1650)