English Russian
Известия
Izvestiya of Altai State
University Journal
The News of Altai State University

 Архив журнала «Известия АлтГУ», начиная с 2017 г., размещен на новой версии сайта http://izvestiya.asu.ru
 Актуальная информация о журнале размещена на новой версии сайта http://izvestiya.asu.ru

Print ISSN 1561-9443
On-line ISSN 1561-9451
Issues list
Table of Contents
Physical science
Mathematics
About the Journal
Editorial board and Editorial advisory board
Regulations on reviewing research papers
Rules of the articles representation
Publication Ethics of the journal «Izvestiya of Altai State University»
 
1-1(85)2015
  PHYSICAL SCIENCE

A.I. Goncharov

Relativistic Dynamics of a Point as an Emergent Phenomenon in a Standing Wave System

In this paper, problems of relativistic kinematics are studied, and a formula of infinite string oscillations U(x, t) = cos Ф(1)(x, t) cos S(x, t) with the phase motion Ф(1) = 0 in accordance with the arbitrarily given law x = X(t) (|v| < c, where v = X; c is the sound velocity) is obtained. The obtained formula allows us to trace the emergence of one-dimensional relativistic dynamics laws for a material point. It is shown that S(x, t) is a solution of Hamilton  Jacobi equation and can be considered as the action of the "particle" with Ф(1) = 0 phase. The phase motion is likely to be influenced by the potential V (x, t) = p(t)(X(t) − x) (where p is a momentum of the velocity v), and obeys the Newton equation and the Hamilton equations. The function ψ = exp (iS) is a solution of the Schrodinger equation with a relativistic Hamiltonian operator with the potential V (x, t), in which the operator √−c22 + m2c4 is expanded into series. In a non-relativistic case with the particle speed vc, this equation coincides with the normal Schrodinger equation. It is demonstrated that the relativistic equation is linked with the one-dimensional Dirac equation in the Foldy  Wouthuysen representation under condition of magnetic field absence. Further, the possibility of complex structure objects introduction in the framework of a linear wave model is investigated.

DOI 10.14258/izvasu(2015)1.1-02

Key words: special relativity, standing waves, dynamics, quantum mechanics

Full text at PDF, 591Kb. Language: Russian.

GONCHAROV A.I.
Altai State University (Barnaul, Russia)
E-mail: goncharov.ai@mail.ru

 

Print Edition of "Izvestiya of Altai State University" © 1996-2017 Altai State University.
All rights reserved. Any of parts of a journal or edition as a whole cannot be reprinted without the written sanction of the authors or publisher. On purchase of a journal to address to ASU publishing house:
Altai State University. 656049, 66 Dimitrova street, Barnaul, Russia. Telephone + 7 (3852) 366351.