Recent content by Feelingfine

I know that in the case of central potential V(r) the hamiltonian of the system always commutes with l^2 operator. But what happends in this case?

My teacher said me this commutator is zero because the spherical harmonics are eigenfunctions of L^2. Actually, he said that any operator must commute with its eigenfunctions. I tried an example: [L^2,Y_20] expressing L^2 on spherical coordinates and I determined this commutator is not zero...