[QUE/QM-10003]

 The spherical harmonics $Y_{lm}(\theta,\phi)$ are normalized simultaneous eigenfunctions of $L^2$ and $L_z$ operators. Use the co-ordinate space expressions \begin{eqnarray*} L_x &=& i\hbar \Big( \sin\phi {\partial\over \partial\theta } + \cot \theta
 \cos\phi{\partial\over \partial \phi} \Big)\\ L_y &=& i\hbar \Big(-\cos\phi {\partial\over \partial\theta } + \cot \theta
 \sin\phi{\partial\over \partial \phi} \Big)\\ L_z &=& -i\hbar {\partial\over\partial \phi} \end{eqnarray*}
\samepage{for the orbital angular momentum operators and the properties of thelladder\\operators, $L^\pm$, and construct expressions for $Y_{lm}(\theta,\phi)$ for $l=2$ and $m=2,1,0,-1,-2$.}