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

Quasipotential approach, suggested by Logunov and Tavkhelidze, is applied t o the description of two-particle systems in quantum field theory. In some important cases this method resulted in integral equations with kernels dep ending upon the total energy of the system. The problem of the numerical solving of these equation is considered. An it eration method of solving this problem is proposed, it is based on successi ve solving of a series of linear eigenvalue problems. The existence and uni ty of received solution and the convergence of iteration process under cert ain conditions are proved. It is shown that integral operators of quasipote ntial equations submit to these conditions. The bound energy spectrum of th e two-particle system in relativistic and nonrelativistic cases is obtained . (C) 2000 Elsevier Science B.V. All rights reserved.