In this PDF document (a lecture by Shivaly Reddy, page 13), he says that
$L^2$ is independent of $r$; therefore it commutes with any function of $r$.
This seems related to a problem in Schaum's Quantum Mechanics (Amazon link) dealing with a particle in a spherical potential well. In the solution, after writing down the Hamiltonian, they say,
It is evident that $[H, L^2] = 0$; hence, we write $\Psi = R(r) \cdot Y_{ml}(\theta,\varphi)$..."
Both sources seem to be saying that when the potential well is spherically symmetric, $[H, L^2] = 0$. Why, exactly?
Schaum goes on to say that since $[H,L^2] = 0$, then we can separate out the radial and angular parts of the wave function. Would you please explain that reasoning also?
