A one-electron atom whose ground state is non degenerate is placed in a uniform electric field in the z-direction. Obtain an approximate expression for the induced electric dipole moment of the ground state by considering the expectation value of ez with respect to the perturbed state vector computed to first order. Show that the same expression can also be obtained from the energy shift ∆ = – α | E |² / 2 of the ground state computed to second order.