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【Clebsh-Gordan係数Memo1】
\begin{equation}
|lsjm\rangle=\sum_{m_{l},m_{s}}C^{~l~s~j}_{m_{l}m_{s}m}|lm_{l}\rangle|sm_{s}\rangle
\end{equation}
$m=m_{l}+m_{s}$、$s=1/2$のとき
\begin{equation}
|lsjm\rangle=C^{~l~\frac{1}{2}~j}_{m-\frac{1}{2},\frac{1}{2},m}Y_{l,m-\frac{1}{2}}\chi_{\frac{1}{2},\frac{1}{2}}+C^{~l~\frac{1}{2}~j}_{m+\frac{1}{2},-\frac{1}{2},m}Y_{l,m+\frac{1}{2}}\chi_{\frac{1}{2},-\frac{1}{2}}
\end{equation}

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