Solutions of a Bethe-Salpeter Equation

Abstract

The discussion in the preceding paper of a simplified Bethe-Salpeter equation is continued. Two methods are used to find a complete set of solutions, an integral transform method, and an adaption of Fock's treatment of the hydrogen atom. The degeneracy is found to be the same as that of the nonrelativistic hydrogen. In addition to the solutions which have the expected nonrelativistic limit, a large number of anomalous solutions are obtained. The behavior in the limit in which the mass of one particle becomes infinite is considered, and it is found that in this limit the ladder approximation gives an equation which does not correspond to the motion of a particle in the field of a fixed center of force.