  It is shown that the radial Schroedinger equation for a power law potential
and a particular angular momentum may be transformed using a change of variable
into another Schroedinger equation for a different power law potential and a
different angular momentum. It is shown that this leads to a mapping of the
spectra of the two related power law potentials. It is shown that a similar
correspondence between the classical orbits in the two related power law
potentials exists. The well known correspondence of the Coulomb and oscillator
spectra is a special case of a more general correspondence between power law
potentials.
