  We study two-particle systems in a model quantum field theory, in which
scalar particles and spinor particles interact via a mediating scalar field.
The Lagrangian of the model is reformulated by using covariant Green's
functions to solve for the mediating field in terms of the particle fields.
This results in a Hamiltonian in which the mediating-field propagator appears
directly in the interaction term. It is shown that exact two-particle
eigenstates of the Hamiltonian can be determined. The resulting relativistic
fermion-boson equation is shown to have Dirac and Klein-Gordon one-particle
limits. Analytic solutions for the bound state energy spectrum are obtained for
the case of massless mediating fields.
