One way to establish which transitions are forbidden is to compute the expectation value...

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

where represents an integral over all space, and ψ_f 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 / = 0 state to another / = 0 state is forbidden. (Transitions considered this way are sometimes called electric dipole transitions, because the electric dipole moment is proportional to .) (Hint: It is helpful to break the vector r into its Cartesian components x, y, and z.)