Express the matrix element ⟨α2 β2 γ2|J3^2| α1 β1 γ1⟩in terms of a series in 𝒟m n^j(αβγ)=⟨αβγ|j m

Question

Accepted Answer

First, we can express the matrix element $u005Cleftu005Clangleu005Calpha_{2} u005Cbeta_{2} u005Cgamma_{2}u005Cleft|J_{3}

Express the matrix element $\left\langle\alpha_{2} \beta_{2} \gamma_{2}\left|J_{3}^{2}\right| \alpha_{1} \beta_{1} \gamma_{1}\right\rangle$ in terms of a series in $$ \mathscr{D}_{m n}^{j}(\alpha \beta \gamma)=\langle\alpha \beta \gamma \mid j m n\rangle . $$