A problem of elastic collision of two spinless particles at their local interaction in relativistic quantum mechanics

Abstract

The earlier definition of the square root of a differential operator leading to a local operator was used to solve the problem of collision of two particles. The problem is posed and solved for the two-particle relativistic Schr¨odinger equation corresponding to the elastic collision of two spinless particles in their local interaction. An elastic collision of particles in a system of the center of momenta is described for a finite radius of interaction. The problem is solved for repulsive and attracting interaction potentials. It is shown that the proposed approach in relativistic quantum mechanics leads to the correct nonrelativistic limit. A transition is made to an arbitrary frame of reference. Refs 22.