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Spherical eigenvalues/functions

  1. Nov 18, 2006 #1
    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.
     
  2. jcsd
  3. Nov 19, 2006 #2
    Anybody have a clue how to go about this? I feel like I should be able to do this but I just can't. I've looked at it for hours and don't know how to begin.. nothing I've tried works. sigh. thanks for the help :)
     
  4. Nov 19, 2006 #3
    Anybody? This should be a straightforward problem, which is what makes it so frustrating :(
     
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