An exactly soluble relativistic quantum two-fermion problem

The two-fermion problem of quantum electrodynamics in which both particles are treated relativistically and full spin degrees of freedom are taken into account is shown to be exactly soluble when potentials up to order ?4 are kept. It is therefore a good starting point for radiative corrections of higher order for the precision tests of QED in bound-state problems. Recoil corrections are included to all orders.