Spacings of Quarkonium Levels with the Same Principal Quantum Number

The spacings between bound-state levels of the Schr"odinger equation with the same principal quantum number $N$ but orbital angular momenta $\mathrm{\ell }$ differing by unity are found to be nearly equal for a wide range of power potentials $V=\lambda r^{\nu }$, with $E_{N \ell} \approx F(\nu, N) - G(\nu,N) \ell$. Semiclassical approximations are in accord with this behavior. The result is applied to estimates of masses for quarkonium levels which have not yet been observed, including the 2P $c\bar{c}$ states and the 1D $b\bar{b}$ states.