Iteration method of solving the integral equation with nonlinear dependence on spectral parameter

Abstract

Quasipotential approach, suggested by Logunov and Tavkhelidze, is applied to the description of two-particle systems in quantum field theory. In some important cases this method resulted in integral equations with kernels depending upon the total energy of the system. The problem of the numerical solving of these equation is considered. An iteration method of solving this problem is proposed. It is based on successive solving of a series of linear eigenvalue problems. The existence and unity of received solution and the convergence of iteration process under certain conditions are proved. It is shown that integral operators of quasipotential equations submit to these conditions. The bound energy spectrum of the two-particle system in relativistic and nonrelativistic cases is obtained.