The perturbed hydrogen atom: some new algebraic results

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