Abstract: In this paper as continuation of our first paper [4], the variational perturbation scheme based on hydrodynamic analogy to Schrödinger equation is adopted and the perturbed wavefunctions for the hydrogen-like atoms H, He⁺, Li⁺², Be⁺³,B⁺⁴ in their excited states (21±1)and (32±2)in a small and time harmonic electric field and the polarizabilities and the 1st resonant frequences are calculated. And the variation of the electronic probability is also discussed. It is shown that the calculated results of the polarizability and the 1st resonant frequence are in good agreement with the exact data. And it is further shown that ∈ and S play the same important role in the calculation of the polarizability using this scheme.

Key words: Hydrodynamic analogy to Schrödinger equation, variational perturbation scheme, excited state