Reduction and Unfolding for Quantum Systems: the Hydrogen Atom
  In this paper we propose a ``quantum reduction procedure'' based on the reduction of algebras of differential operators on a manifold. We use these techniques to show, in a systematic way, how to relate the hydrogen atom to a family of quantum harmonic oscillators, by the means of the Kustaahneimo-Stiefel fibration. 
A. D'Avanzo, G. Marmo, A. Valentino