Hydrogen supersymmetry: A new method in perturbation theory

TL;DR

This paper introduces a novel perturbation theory method leveraging hydrogen atom supersymmetry to simplify calculations, demonstrated through high-order polarizability computations in electric fields.

Contribution

It presents a new perturbation approach based on hydrogen supersymmetry, enabling straightforward eigenvalue problem solutions for perturbed systems.

Findings

Complete basis constructed from bound states

Eigenvalue problem with equidistant spectrum

High-order polarizability calculated successfully

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.