Algebraic solution of the supersymmetric hydrogen atom in d dimensions

摘要

In this paper the N = 2 supersymmetric extension of the Schrodinger 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. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 28]