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

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

Problems of Two-particle Reaction and Decay of Neutral Particle in Relativistic Quantum Mechanics


Vladimir Meerovich Lagodinskiy

Candidate of Science in Physics and Mathematics, docent,
associate Professor of Department of applied mathematics,
Saint-Petrsburg State University of aerospace instrumentation
67, lit. A, Bolshaya Morskaya, Saint-Petrsburg, 190000, Russia


Two boundary value problems for a system of two relativistic Schrodinger equations, which are differential equations of infinite order, are set and solved. This system describes the interaction of spinless particles in relativistic quantum mechanics. The first problem describes the scattering of two spinless particles accompanied by the appearance of an intermediate spinless particle, and the other problem -- the decay of a spinless particle. It is shown that under the set boundary conditions the problems are self-adjoint, the particle flows are continuous, and the spectra of these problems are bounded below. Thus, unlike the theory based on the Klein-Gordon equation, in this approach the solutions corresponding to the states of free particles with negative energies do not occur. The dependences of the effective cross-section of two-particle scattering and the decay constant of a spinless particle on the energy are obtained. The solutions are accurate within the accepted model.



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