Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions

Abstract

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.

36 pages, 6 figures

References in corpus (1)

• The classical supersymmetric Coulomb problem

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