クレブシュ–ゴルダン係数
.. j 2 ) {\displaystyle |j_{1}m_{1}\rangle |j_{2}m_{2}\rangle \equiv |j_{1}m_{1}\rangle \otimes |j_{2}m_{2}\rangle \quad (m_{1}=-j_{1},\ldots j_{1},\quad m_{2}=-j_{2},\ldots j_{2})}
V 12 {\displaystyle V_{12}} で作用する角運動量演算子は以下で定義される。
( j i ⊗ 1 ) | j 1 m 1 ⟩ | j 2 m 2 ⟩ ≡ ( j i | j 1 m 1 ⟩ ) ⊗ | j 2 m 2 ⟩ {\displaystyle ({\textrm {j}}_{i}\otimes 1)|j_{1}m_{1}\rangle |j_{2}m_{2}\rangle \equiv (j_{i}|j_{1}m_{1}\rangle )\otimes |j_{2}m_{2}\rangle }
( 1 ⊗ j i ) | j 1 m 1 ⟩ | j 2 m 2 ⟩ ≡ | j 1 m 1 ⟩ ⊗ j i | j 2 m 2 ⟩ ( i = x , y , z ) {\displaystyle (1\otimes {\textrm {j}}_{i})|j_{1}m_{1}\rangle |j_{2}m_{2}\rangle \equiv |j_{1}m_{1}\rangle \otimes j_{i}|j_{2}m_{2}\rangle \quad \quad (i=x,y,z)}