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Русская версия

**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

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.

- differential equations of infinite order
- relativistic quantum mechanics

- Bjorken J. D., Drell S. D.
*Relativistic quantum mechanics.*McGraw-hill. 1964. 297p - Itzykson C., Zuber J. -B.
*Quantum field theory.*McGraw-hill. 1980. 448p - Dirac P. A. M.
*The principals of quantum mechanics.*Oxford. 1930. 408p - Olver P. J.
*Applications of Lie groups to d[fferential equations.*Springer-Verlag. 1989. 635p - V. Neuman J
*. Mathematische grundlagen der quantenmechanik.*Springer-Verlag. 1932. 367p - Richmayer R. D.
*Principles of advanced mathematical physics. V1.*Springer-Verlag. 1978. 186p - Treves F.
*Introduction to pseudodifferential and Furierintegral operators. V1. Pseudodifferential operators.*Plenum Press. 1982. 180p - Lagodinskiy V. M.
*Golomorfical function of differential operators and differential equtions of infinit order.*Cand. Diss. SPb. 2005. 110p - Golovin A. V., Lagodinskiy V. M.
*A problem of elastic collision of two spinless particles at their local interection in relativistic quantum mechanics.*Vestnic SPbSU ser. 4 Physics, Chemistry, 2017, T. 4(62), v. 3, p. 249-263