An electron in the Coulomb field of the proton is in the state
∣ψ⟩=54∣1,0,0⟩+53i∣2,1,1⟩
where ∣n,l,m⟩ are the usual energy eigenstates of hydrogen.
(a) What is ⟨E⟩ for this state? What are ⟨L2⟩ and ⟨Lz⟩?
(b) What is ∣ψ(t)⟩? Which of the expectation values in (a) vary with time?