An approximate wave function ψk(0) is operated on by the operators λ-H and (H-λ)-1, where H is the Hamiltonian operator of the quantum system under consideration. We have shown that, if the resulting function φk is continuous, finite and square integrable in the whole domain of the variables of H, it is a better approximate wave function to the eigenstate ψk of the system than ψk(0) is. The expecting value of H, calculated with φk as wave function approaches to that calculated by the method of second order perturbation with ψk(0) as unperturbated states. Polarizabilities of hydrogen-like ions are calculated and good results are obtained.