OK, I have that a particle of mass m is moving on the surface of a sphere of radius R but is otherwise free. The Hamiltonian is H = L^2/(2mR^2). All I have to do is find the energies and wavefunctions of the stationary states... this seems like it should be really easy, but I am struggling mightily for some reason. To be honest I don't even know how to get started.. I know eigenfunctions of Lz are also eigenfunctions of L^2. I know L^2 operating on [tex]Y^m_l[/tex] is [tex]\hbar^2l(l+1)Y^m_l[/tex]. I know once I get one stationary state I should be able to get the rest by operating the raising and lowering operators on it. But I just don't know how to get there. :( Thanks as always for the help.