Significance of relativistic wave equations for bound states

We scrutinize the relevance of relativistic wave equations for the description of quark-antiquark bound states. By comparing the predictions of the nonrelativistic Schroedinger equation (with only the lowest-order relativistic corrections of the famous Breit-Fermi Hamiltonian), the spinless Salpeter equation, and a new semirelativistic wave equation (which incorporates relativistic kinematics and the complete relativistic corrections to the static interaction potential) for light and heavy quarkonia within three different potential models, we discuss the extent to which the use of relativistic wave equations is reasonable or necessary in order to reproduce the experimentally observed meson mass spectra. We are forced to conclude that---contrary to one's physical intuition---a relativistic treatment of bound states in a potential model provides no improvement at all compared to the corresponding nonrelativistic description