How Do You Find the Energies and Wavefunctions for a Particle on a Sphere?

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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 Y^m_l is \hbar^2l(l+1)Y^m_l. 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.
 
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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 :)
 
Anybody? This should be a straightforward problem, which is what makes it so frustrating :(
 

Thread 'Modeling a graph that shows age in relation to depth of an ice sample'

To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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