Solving a Relativistic Quasipotential Equation for a Superposition of a Nonlocal Separable and a Local Quasipotential

摘要

Within the relativistic quasipotential approach to quantum field theory, a method is developed for solving a finite-difference quasipotential equation for the case where a total quasipotential describing the interaction of two relativistic spinless particles of unequal masses is a superposition of a nonlocal separable and a local quasipotential. The cases are investigated where the local component of the total interaction—it is assumed to be known—either admits or does not admit the existence of bound states. This makes it possible to obtain an exact expression for the increment of the phase shift, to determine the conditions of the existence of bound states, and to give a generalization of the Levinson theorem.