A maximally superintegrable deformation of the N-dimensional quantum Kepler-Coulomb system

Abstract

The N-dimensional quantum Hamiltonian Ĥ = -ℏ2|q|/ 2(η+|q|) dtri;2 - k/η+|q| is shown to be exactly solvable for any real positive value of the parameter η. Algebraically, this Hamiltonian system can be regarded as a new maximally superintegrable η-deformation of the N-dimensional Kepler-Coulomb Hamiltonian while, from a geometric viewpoint, this superintegrable Hamiltonian can be interpreted as a system on an N-dimensional Riemannian space with nonconstant curvature. The eigenvalues and eigenfunctions of the model are explicitly obtained, and the spectrum presents a hydrogen-like shape for positive values of the deformation parameter η and of the coupling constant k. © Published under licence by IOP Publishing Ltd.