Bound State Equations and Heavy Quark Interactions.

The predictions of several bound state equations with a variety of interactions are compared with heavy quark bound state data in an attempt to constrain and better understand the nature of the actual quark-antiquark interaction. The phenomenological applications of several theoretically motivated potential energies, including a potential energy that exhibits the full content of perturbative QCD at small radii, are examined using a spinless Schrodinger equation. The effect of using a relativistic kinetic energy is tested by comparing the phenomenological success of the Schrodinger equation with the spinless Salpeter equation. The relativistic equation better accounts for the observed energy levels and gives improved results for s and p-wave annihilation rates and E1 transitions. An approach to the spin-dependent quarkonium problem is developed based on the reduced Salpeter equation with an instantaneous, local interaction. A vector-scalar interaction, based on the perturbative QCD potential energy, is shown to satisfactorily account for the observed heavy meson masses. However, the meson masses cannot distinguish QCD from non-QCD interactions. A general numerical method for the solution of eigenvalue equations is presented and shown to yield rapid, accurate solutions to all the bound state equations considered.