.

(restored equation*)

$$L_x = -\imath \hbar \left ( \sin \phi \frac{\partial}{\part... ...\cos \phi}{\sin\theta} \frac{\partial}{\partial \phi} \right )$$ (16)

and

$$L_y \equiv z p_x - xp_z = -\imath \hbar r \cos \theta \left ( \si... ... \frac{\sin \phi}{r \sin \theta}\right )\frac{\partial}{\partial \phi} \right )$$

$$-\imath \hbar r \sin \theta \cos \phi \left ( \cos \theta \frac{\... ...l}{\partial \theta} + \left ( 0 \right )\frac{\partial}{\partial \phi} \right )$$ (17)

which becomes

$$L_y = -\imath \hbar \left ( \left ( \frac{r \cos^2 \theta \cos \p... ...theta \sin \phi}{r \sin \theta}\right ) \frac{\partial}{\partial \phi} \right )$$

$$-\imath \hbar \left ( \left ( \frac{r\sin^2 \theta\cos \phi} {r} \right ) \frac{\partial}{\partial \theta} \right )$$ (18)

so that

$$L_y = -\imath \hbar \left ( \cos \phi \frac{\partial}{\partia... ...eta \sin \phi}{\sin K} \frac{\partial}{\partial \phi} \right )$$