The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$.

Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that the expectation value of angular momentum does not change with time.

Expectation value of angular momentum, $\langle \hat{L} \rangle$ = $\langle \psi \mid \hat{L} \mid \psi \rangle $ where $\psi$ is a generic wavefunction.