Approximate Solution of the Bethe-Salpeter Equation for Two Fermions

The eigerfunction and the binding energy of the ground state are obtained for a bound state of two fermions, which interact through photons or scalar photons in the ladder approximation. The Bethe-Salpeter equation is separated into four independent sets of equations by applying the Tani-Foldy- Wouthuysen transformations. These equations are further simplified by neglecting part of the recoil. Retardation is completely taken into account. The wave function is expanded in a form convenient for obtaining spin singlet and triplet solutions. As an example, the ground state of positronium is solved. (auth)