Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions

Details Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions

2002-08-30

arxiv.org/abs/hep-th/0208228v2

Annals Phys. 303 (2003) 359-388

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, 6 figures

Scientific paper

10.1016/S0003-4916(03)00003-4

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.

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