Exact solutions of Bethe-Salpeter equations with instantaneous interactions

The Bethe-Salpeter approach allows for quantum-field theoretic descriptions of relativistic bound states; its inherent complexity, however, usually prevents the finding of exact solutions. Under suitable simplifying assumptions about the systems discussed, we derive analytically examples of rigorous solutions to the instantaneous homogeneous Bethe-Salpeter equation by relating tentative solutions to the interactions responsible for the formation of bound states.