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

Abstract

The N-dimensional quantum Hamiltonian (H) over cap =-h(2)vertical bar q vertical bar/2(eta +vertical bar q vertical bar del(2) - k/eta + vertical bar q vertical bar is shown to be exactly solvable for any real positive value of the parameter eta. Algebraically, this Hamiltonian system can be regarded as a new maximally superintegrable eta-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 eta and of the coupling constant k