(a) For the wave function (r, , ) = R(r) O () () with () = Ae im show that | |2 is independent of

(a) For the wave function ψ(r, θ, Φ) = R(r) O (θ) Φ (Φ) with Φ (Φ) = Ae imΦ show that | ψ |2 is independent of Φ.
(b) What value must A have if Φ (Φ) is to satisfy the normalization condition f0 |Φ (Φ)2 dΦ = 1?