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NONRELATIVISTIC BEREZIN - MARINOV MODEL WITH HYPERFINE INTERACTION

Abstract

Pseudo-classical Berezin - Marinov model with two charged particles carrying ½ spin is considered. The motion equations in Grassmann as well as in classical (“observable”) variables are obtained. The true integrals of motion are determined and the orbital motion is shown to remain Kepler. However the complete description of the spatial motion includes the Grassmann (nilpotent) component, which leads to the observed effects only after application of the averaging procedure with the use of Berezin - Marinov phase space density. Under special choice of central potentials the system considered gives a pseudo-classical description to the hydrogen atom with the hyperfine interaction considered. The particular case of complete integrability of the electron radial motion is described.

About the Authors

S. L. Lebedev
Surgut State University
Russian Federation


V. V. Tereshchenko
Surgut State University
Russian Federation


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Review

For citations:


Lebedev S.L., Tereshchenko V.V. NONRELATIVISTIC BEREZIN - MARINOV MODEL WITH HYPERFINE INTERACTION. Proceedings in Cybernetics. 2017;(4 (28)):100-106. (In Russ.)

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ISSN 1999-7604 (Online)