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Wigner 3-j symbols : ウィキペディア英語版
3-j symbol
In quantum mechanics, the Wigner 3-j symbols, also called 3''j'' or 3''-jm'' symbols,
are related to Clebsch–Gordan coefficients
through
:
\begin
j_1 & j_2 & j_3 \\
m_1 & m_2 & m_3
\end
\equiv
\frac}
\langle j_1 \, m_1 \, j_2 \, m_2 | j_3 \, (-m_3) \rangle.

== Inverse relation ==

The inverse relation can be found by noting that is an integer and making the substitution :
:
\langle j_1 \, m_1 \, j_2 \, m_2 | j_3 \, m_3 \rangle
= (-1)^ \sqrt
\begin
j_1 & j_2 & j_3 \\
m_1 & m_2 & -m_3
\end
.
Note that the exponent of the sign factor is always an integer, therefore it remains the same under inversion.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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