回転準位
角運動量演算子 L ^ a {\displaystyle {\hat {L}}_{a}} , L ^ b {\displaystyle {\hat {L}}_{b}} , L ^ c {\displaystyle {\hat {L}}_{c}} から L ^ 2 {\displaystyle {\hat {\boldsymbol {L}}}^{2}} を計算すると
− 1 ħ 2 L ^ 2 = 1 sin  β ∂ ∂ β ( sin  β ∂ ∂ β ) + 1 sin 2  β ( ∂ 2 ∂ α 2 + ∂ 2 ∂ γ 2 ) − 2 cos  β sin 2  β ∂ 2 ∂ α ∂ γ {\displaystyle \ -{\frac {1}{\hbar ^{2}}}{\hat {\boldsymbol {L}}}^{2}={\frac {1}{\sin \beta }}{\frac {\partial }{\partial \beta }}\left(\sin \beta {\frac {\partial }{\partial \beta }}\right)+{\frac {1}{\sin ^{2}\beta }}\left({\frac {\partial ^{2}}{\partial \alpha ^{2}}}+{\frac {\partial ^{2}}{\partial \gamma ^{2}}}\right)-{\frac {2\cos \beta }{\sin ^{2}\beta }}{\frac {\partial ^{2}}{\partial \alpha \partial \gamma }}}