Solution of two-body relativistic bound-state equations with confining plus Coulomb interactions

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus linear confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound-state problem. Such a treatment is most easily carried out in momentum space. However, the position-space linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities [ital exactly] and thereby solve the Schroedinger equation in momentum space for [ital all] partial waves. Furthermore, we generalize the linear and Coulomb potentials to relativistic kernels in four-dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three-dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus confining interactions for all partial waves.