Formula_9272

\[\left.\begin{array}{c}\hat{\boldsymbol{L}}^{2} \psi=-\hbar^{2}\left\{\frac{1}{\sin \theta} \frac{\partial}{\partial \theta}\left(\sin \theta \frac{\partial}{\partial \theta}\right)+\frac{1}{\sin ^{2} \theta} \frac{\partial}{\partial \varphi^{2}}\right\} \psi=\lambda \psi, \\\hat{L}_{z} \psi=-i \hbar \frac{\partial \psi}{\partial \varphi}=\mu \psi,\end{array}\right\}\]