The interaction potential with the form as V(x)= x2+λx2/(1+gx2) where g >0, appears in several areas of laser theory, quantum field theory, atom and nuclear physics. One could consider that the solution of the eigenequation either by the classical Rayleigh-Schr?dinger perturbation scheme or by the perturbed ladder operators scheme. Nevertheless, the perturbation series does not converge for any values of λ and g. In the present paper, it is shown that this difficulty can be overcome as long as the potential function can be expanded in a convergent series on the basis ofthe Hermite polynomials. Therefore, the eigenequation ((d2)/(dx2)-V(x)+ξ)φ(x)=0,∞2)/(dX2)-b2X2-Σkc2kH2k(b1/2X)+ξ)φ(X)=0.