[en] A new iteration procedure for solution of the Schroedinger equation with arbitrary potential is proposed. Both the eigenvalues and eigenfunctions are represented in the form of a series which is well convergent under certain conditions. The solution of the K-dimensional Schroedinger equation within the proposed scheme reduces to a problem of the k-dimensional electrostatics. As an example potentials xsup(2n) (n=2,3,4) and m²x²+gx⁴ in an one-dimensional space are considered. It is shown that closed analytical expressions for corrections at all orders of the perturbation theory can be derived