  Besides the standard quantum version of the Coulomb/Kepler problem, an
alternative quantum model with not too dissimilar phenomenological (i.e.,
spectral and scattering) as well as mathematical (i.e., exact-solvability)
properties may be formulated and solved. Several aspects of this model are
described. The paper is made self-contained by explaining the underlying
innovative quantization strategy which assigns an entirely new role to
symmetries.
