.

(*restored equation*) To continue, we need to obtain the ladder operators in the $\theta$, $\phi$, r form, From Equations 16 through 22 we have

$$L_x +\imath L_y = \imath \hbar \left ( \sin \phi \frac{\par... ...\sin \phi}{\sin\theta} \frac{\partial}{\partial \phi} \right )$$ (47)

Grouping by partial derivatives we obtain

$$L_x +\imath L_y = \left ( \imath \hbar \sin \phi + \hbar \co... ...- \hbar \cot \sin \phi \right ) \frac{\partial}{\partial \phi}$$

which is,

$$L_x +\imath L_y = \hbar\left ( \imath \sin \phi + \cos \phi ... ...- \sin \phi \right )\cot \theta \frac{\partial}{\partial \phi}$$

i.e.,

$$L_x +\imath L_y = \hbar\left ( \imath \sin \phi + \cos \phi ... ...th\sin \phi \right )\cot \theta \frac{\partial}{\partial \phi}$$