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\begin{equation}
|j_{1}j_{2}jm\rangle=|j_{1}m_{1}\rangle|j_{2}m_{2}\rangle=\sum_{m_{1},m_{2}}|j_{1}j_{2}m_{1}m_{2}\rangle\underbrace{\langle j_{1}j_{2}m_{1}m_{2}|j_{1}j_{2}jm\rangle}_{\mathrm{C-G係数}}
\end{equation}
$\langle j_{1}j_{2}j^{\prime}m^{\prime}|j_{1}j_{2}jm\rangle=\delta_{jj^{\prime}}\delta_{mm^{\prime}}$より
\begin{equation}
\sum_{m_{1},m_{2}}C^{\ast j_{1}~j_{2}~j^{\prime}}_{m_{1}m_{2}m^{\prime}}C^{~j_{1}~j_{2}~j}_{m_{1}m_{2}m}=\delta_{jj^{\prime}}\delta_{mm^{\prime}}
\end{equation}

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