The perturbed hydrogen atom: some new algebraic results

Abstract

We have employed algebraic methods to calculate the bound-state spectra of a non-relativistic hydrogen atom subjected to a wide class of perturbations. Our procedure exploits the linearity of the complete (perturbed) Hamiltonian in the generators of the S0(2,2) Lie algebra which follows naturally from the separation of variables in Schrodin- ger's equation in parabolic coordinates. Appropriate transformations then allow the Hamil- tonian to be expressed as a linear combination of the compact generators of the two underlying SO(2, 1) algebras. We give some examples for which the bound-state spectra can be obtained completely analytically.