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Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions

A. Kirchberg·J. D. Laenge·P. A. G. Pisani·A. Wipf
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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.

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A. Kirchberg, J. D. Laenge, P. A. G. Pisani, A. Wipf. 2002-09-30. Algebraic Solution of the Supersymmetric Hydrogen Atom in d Dimensions. https://doi.org/10.1016/s0003-4916(03)00003-4

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