  The $e^-$-$e^+$ bound state spectrum of QED3 is investigated in the quenched
ladder approximation to the homogeneous Bethe-Salpeter equation with fermion
propagators from a rainbow approximation Schwinger-Dyson equation. A detailed
analysis of the analytic structure of the fermion propagator is performed so as
to test the appropriateness of the methods employed. The large fermion mass
limit of the Bethe-Salpeter equation is also considered, including a derivation
of the Schr\"{o}dinger equation, and comparisons made with existing
non-relativistic calculations.

High Energy Physics - Theory