Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions
  In this paper the N=2 supersymmetric extension of the Schroedinger Hamiltonian with 1/r-potential in arbitrary space-dimensions is constructed. The supersymmetric hydrogen atom admits a conserved Laplace-Runge-Lenz vector which extends the rotational symmetry SO(d) to a hidden SO(d+1) symmetry. This symmetry of the system is used to determine the discrete eigenvalues with their degeneracies and the corresponding bound state wave functions. 
A. Kirchberg, J.D. Laenge, P.A.G. Pisani and A. Wipf