2. Prove that the Hamiltonian \hat{H} for a spherically symmetric potential (so $V = V(r)$ only) commutes with the angular momentum operator \hat{L} and they therefore share eigenstates $|n\ell m\rangle$. Hint: Show that \hat{L}_z commutes with \hat{p}^2 and \hat{r}^2 and go from there.
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