(Solved): 3) The angular momentum operator for a particle moving in a circle is: lz=idd Are ...

3) The angular momentum operator for a particle moving in a circle is: $\widehat{l_z}=?i?\frac{d}{d?}$ Are the wave functions ${?}_m(?)$ eigenfunctions of the operator $\widehat{l_z}$ ? If so, what are the corresponding eigenvalues? 4) Are the functions $f(x,y)=x$ and $g(x,y)=y$ eigenfunctions of $\widehat{l_z}$ ? Hint: Consider that $x=r\cos (?)$ and $y=r\sin (?)$, where $r$ is the fixed radius of the circle that the particle is confined to move in.