Consider a particle whose wave function is given by ψ(x,y,z)=A[(x+z)y+z2]/r2−A/3, where A is a constant.
(a) Is ψ an eigenstate of L^2? If yes, what is the corresponding eigenvalue? Is it also an eigenstate of L^z?
(b) Find the constant A so that ψ is normalized.
(c) Find the relative probabilities for measuring the various values of L^z and L^2, and then calculate the expectation values of L^z and L^2.
(d) Calculate L^±∣ψ⟩ and then infer ⟨ψ∣L^±∣ψ⟩.