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.

(restored equation*)

$\begin{displaymath} L_y = -\imath \hbar \left ( \cos \phi \frac{\partial}{\parti... ...\sin \phi}{\sin\theta} \frac{\partial}{\partial \phi} \right ) \end{displaymath}$

(19)

Finally, for L_z we have

l_z = xp_y-yp_x

which is

$\begin{displaymath}-\hbar r \left (\sin \theta \cos \phi \frac{\partial}{\partial y} - \sin \theta \sin \phi \frac{\partial}{\partial x}\right ) \end{displaymath}$

(20)

which becomes

$\displaystyle -\hbar r \left (\sin \theta \cos \phi \left (\sin \theta \sin \ph... ... \frac{\cos \phi}{r \sin \theta}\right )\frac{\partial}{\partial \phi} \right .$
$\displaystyle \left . - \sin \theta \sin \phi \left ( \sin \theta \cos \phi\rig... ... \frac{\sin \phi}{r \sin \theta}\right )\frac{\partial}{\partial \phi} \right )$			(21)

$\begin{displaymath} L_z = -\imath \hbar \frac{\partial}{\partial \phi} \end{displaymath}$

(22)

2001-12-26