  The O(4) supersymmetry of the hydrogen atom is utilized to construct a
complete basis using only the bound state wave functions. For a large class of
perturbations, an expansion of the electron (exciton) wave function into such a
complete set reduces the perturbed Schroedinger equation to a standard
eigenvalue problem with an equidistant unperturbed spectrum. A high-order
polarizability of the ground state of the hydrogen atom in a static electric
field is calculated via Rayleigh-Schroedinger perturbation theory for
illustration of the new method.
