Show that for a real wave function ψ(x), the expectation value of momentum ⟨P⟩=0. (Hint: Show that the probabilities for the momenta ±p are equal.) Generalize this result to the case ψ=cψr, where ψr is real and c an arbitrary (real or complex) constant. (Recall that ∣ψ⟩ and a∣ψ⟩ are physically equivalent.)