A New Method for Solving the Bethe–Salpeter Equation

The Bethe–Salpeter equation in the coordinate representation, which has the form of a differential equation of fourth order for the Bethe–Salpeter amplitude is investigated. For the model of scalar particles interacting through exchange of a scalar mass particle, a method for solving it is proposed. The coupling constants and amplitudes as a function of the bound state mass are found. The found coupling constants are compared with those obtained in other approaches.