ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

About the Possibility of Invariant Description of the Local Two-particle Interaction in Relativistic Quantum Mechanics


Vladimir Meerovich Lagodinskiy

PhD in physics and mathematics
Dept. of applied mathematics
Saint-Petersburg State University
of aerospace instrumentation
Bolshaia Morskaia str. 67,
190000, Saint-Petersburg, Russia


In this work it is shown that the relativistic two-particle Schrodinger equation, which is a differential equation of infinite order, yields the relativistic invariant description of the system of two spinless particles interacting through a spherically symmetric short-range potential. A change of independent variables based on the Lorentz transformations is found. This change leads to a set of variables which describe both the interaction of particles in an inertial reference frame (center pulses system,where the sum of particles momenta equals zero), and the motion of the center pulse in the source frame of reference. These variables are separated, which leads to a self-adjoint boundary value problem.



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