The N-dimensional quantum Hamiltonian
Hˆ = −
~
2
|q|
2(η + |q|)
∇
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.
