  Bound-state solutions of the singular harmonic oscillator and singular
Coulomb potentials in arbitrary dimensions are generated in a simple way from
the solutions of the one-dimensional generalized Morse potential. The
nonsingular harmonic oscillator and nonsingular Coulomb potentials in arbitrary
dimensions with their additional accidental degeneracies are obtained as
particular cases. Added bonuses from these mappings are the straightforward
determination of the critical attractive singular potential, the proper
boundary condition on the radial eigenfunction at the origin and the
inexistence of bound states in a pure inversely quadratic potential.
