A hydrogen atom starts out in the following linear combination of the stationary states n=2, ℓ=1, m=1 and n=2, ℓ=1, m=−1:
Ψ(r,0)=21(ψ211+ψ21−1).
(a) Construct Ψ(r,t). Simplify it as much as you can.
(b) Find the expectation value of the potential energy, ⟨V⟩. (Does it depend on t?) Give both the formula and the actual number, in electron volts.