  The relativistic two-body system in (1+1)-dimensional quantum electrodynamics
is studied. It is proved that the eigenvalue problem for the two-body
Hamiltonian without the self-interaction terms reduces to the problem of
solving an one-dimensional stationary Schr\"odinger type equation with an
energy-dependent effective potential which includes the delta-functional and
inverted oscillator parts. The conditions determining the metastable energy
spectrum are derived, and the energies and widths of the metastable levels are
estimated in the limit of large particle masses. The effects of the
self-interaction are discussed.

High Energy Physics - Theory