One way to establish which transitions are forbidden is to compute the expectation value of the electron’s position vector r using wave functions for both the initial and final states in the transition. That is, compute
∫ψf∗r ψ i dτ
where ∫dτ represents an integral over all space, and ψf​ and ψ i​
are the final and initial states. If the value of the integral is zero, then the transition is forbidden. Use this procedure to show that a transition from one (l=0) state to another (l=0) state is forbidden. (Hint: It is helpful to break the vector (r) into its Cartesian components x, y, and z.)