Hydrogen Supersymmetry: A New Method in the 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 Schrö dinger equation to the ordinary eigenvalue problem with equidistant unperturbed energy spectrum. A high-order polarizability of the ground state of the hydrogen atom in a static electric field is calculated via the Rayleigh-Schrö dinger perturbation theory for illustration of the new method.