(a) Prove that for a particle in a potential V(r) the rate of change of the expectation value of the orbital angular momentum L is equal to the expectation value of the torque:
dtd⟨L⟩=⟨N⟩,
where
N=r×(−∇V).
(This is the rotational analog to Ehrenfest's theorem.)
(b) Show that d⟨L⟩/dt=0 for any spherically symmetric potential. (This is one form of the quantum statement of conservation of angular momentum.)