About the Possibility of Invariant Description of the Local Two-particle Interaction in Relativistic Quantum Mechanics
Author(s):
Vladimir Meerovich Lagodinskiy
PhD in physics and mathematics
Assoc.Professor
Dept. of applied mathematics
Saint-Petersburg State University
of aerospace instrumentation
Bolshaia Morskaia str. 67,
190000, Saint-Petersburg, Russia
lagodinskiy@mail.ru
Abstract:
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.
Keywords
- differential equations of infinite order
- relativistic quantum mechanics
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