On the solution of the relativistic quasipotential equation for the superposition of a local potential and of the sum of nonlocal separable quasipotentials

Abstract

A solution has been found for the finite-difference quasipotential equation with the total quasi-potential that describes the interaction of two relativistic spinless particles of unequal mass. The total interaction, which is the superposition of a local potential and of the sum of nonlocal separable quasi-potentials, is centrally symmetric, does not depend on energy, and admits existence of true bound states. The treatment has been performed in the context of the relativistic quasipotential approach to quantum field theory. Exact expressions for the phase shift increments have been found and their properties have been investigated, the conditions for existence of bound states have been determined, and a generalization of the Levinson theorem is given.