Algebraic Solution of the d-dimensional Coulomb Problem and its Supersymmetric Generalization

A. KIRCHBERG, J.D. LAENGE, P.A.G. PISANI AND A. WIPF

Santiago de Chile

Congreso; Relativistic Quantum Coulomb Systems; 2002

Pontificia Universidad Católica de Chile

The N=2 supersymmetric extension of the Schrödinger 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.