Angular Momentum and Hamiltonian Commutation

[jtgurkin]

I am working on a problem for homework and am supposed to show that the angular momentum operator squared commutes with H and that angular momentum and H also commute. This must be done in spherical coordinates and everything I see says "it's straightforward" but I don't see it. At least not yet. Can someone help?

 

[xman]

I would suggest considering the eigenvalues for both the angular momentum and square of the angular momentum operator. Then think about which parts of either angular momentum (squared or not squared) operator act on the components of the Hamiltonian. Finally, what does the commutation relation tell you about when the operator commutes with the Hamiltonian? I think you should find the problem is actually straight forward, just a little different when you first see it.