Properties of Bethe--Salpeter wave functions for electromagnetically interacting charged scalar particles

The problem of the Bethe-Salpeter equation for two scalar mesons of equal mass, interacting electromagnetically, is considered in the Landau gauge. A spectral-function representation, depending on two variables, is introduced for the case of arbitrary angular momentum and coupling strength. In the limit of strong binding, a simple momentum-space form of the equations is derived, and the eigenvalues and eigenfunctions are obtained for $l=0, 1$.