Hydrogen supersymmetry: A new method in perturbation theory

Abstract

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.