3j記号
( 2 j + 1 ) ∑ m 1 m 2 ( j 1 j 2 j m 1 m 2 m ) ( j 1 j 2 j ′ m 1 m 2 m ′ ) = δ j j ′ δ m m ′ . {\displaystyle (2j+1)\sum _{m_{1}m_{2}}{\begin{pmatrix}j_{1}&j_{2}&j\\m_{1}&m_{2}&m\end{pmatrix}}{\begin{pmatrix}j_{1}&j_{2}&j'\\m_{1}&m_{2}&m'\end{pmatrix}}=\delta _{jj'}\delta _{mm'}.}
∑ j m ( 2 j + 1 ) ( j 1 j 2 j m 1 m 2 m ) ( j 1 j 2 j m 1 ′ m 2 ′ m ) = δ m 1 m 1 ′ δ m 2 m 2 ′ . {\displaystyle \sum _{jm}(2j+1){\begin{pmatrix}j_{1}&j_{2}&j\\m_{1}&m_{2}&m\end{pmatrix}}{\begin{pmatrix}j_{1}&j_{2}&j\\m_{1}'&m_{2}'&m\end{pmatrix}}=\delta _{m_{1}m_{1}'}\delta _{m_{2}m_{2}'}.}