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Journal of Experimental and Theoretical Physics

Behavior of relativistic particles in the field of a deep potential well

G. K. Artimovich, V. I. Ritus, P. J. Shepherd

Published Sep 1, 1993• 0 citations
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For relativistic particles with spin-0 (satisfying the Klein-Gordon equation) and spin-1/2 (satisfying the Dirac equation) in infinitely deep potential well, matrix elements for the coordinate, momentum and the velocity operators are calculated. In the limit of large quantum numbers, these matrix elements give the corresponding classical quantities (nowbeing related quantities in special relativity) and satisfy exact classical relations. These results show that the Heisenberg correspondence principle is applicable to such relativistic systems.
The analysis of the behavioral trend of particle using Klein-Gordon and Dirac equation that was minimally coupled to electromagnetic wave four-vector potential has been carried out. In the analysis, it was clearly observed that each of them has non-relativistic limit at one stage or the other and based on this limitation, there is a great challenge posed on the idea of single particle interpretation since in each case there is a particle and an antiparticle. It therefore reveals the fact that there is no conceptually real existence of single particle in isolation when it comes to relativistic quantum mechanics for any of the equations being used to study the interaction of particle with electromagnetic field.