  A mapping is obtained relating analytical radial Coulomb systems in any
dimension greater than one to analytical radial oscillators in any dimension.
This mapping, involving supersymmetry-based quantum-defect theory, is possible
for dimensions unavailable to conventional mappings. Among the special cases is
an injection from bound states of the three-dimensional radial Coulomb system
into a three-dimensional radial isotropic oscillator where one of the two
systems has an analytical quantum defect. The issue of mapping the continuum
states is briefly considered.
