Comparing the Schrödinger and spinless Salpeter equations for heavy-quark bound states

Abstract

We develop a unified approach to the solution of the Schrödinger and the spinless Salpeter equations. By adjusting the potential and quark masses to best account for the spin-averaged energy levels, we can compare in a realistic way the effect of using a relativistic kinetic energy. Emphasis is given to consideration of relativistic wave-function corrections. We find that the relativistic equation better accounts for the observed energy levels and gives improved results for s- and p-wave annihilation rates and E1 transitions.