A simple interpolation formula for the spectra of power-law and log potentials

Non-relativistic potential models are considered of the pure power V(r) = s gn(q) r(q) and logarithmic V(r) = In(r) types. It is shown that, from the s pectral viewpoint, these potentials are actually in a single family. The lo g spectra can be obtained from the power spectra by the limit q --> 0 taken in a smooth representation P-nl(q) for the eigenvalues E-nl(q). A simple a pproximation formula is developed which yields the first 30 eigenvalues wit h an error less than 0.04%.