Related papers: Coulomb problem for classical spinning particle

Coulomb problem for classical spinning particle

URL: http://arxiv.org/abs/2303.16614v2
Date: Wed, 10 May 2023 14:20:46 GMT
Title: Coulomb problem for classical spinning particle
Authors: Dmitry S. Kaparulin and Nikita A. Sinelnikov
Abstract summary: We consider a weakly relativistic charged particle with an arbitrary spin in central potential $e/r$ in terms of classical mechanics. We show that the spin-orbital interaction causes the precession of the plane of orbit around the vector of total angular momentum. The effective potential for in-plane motion is central, with the corrections to Coulomb terms coming from spin-orbital interaction.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We consider a motion of a weakly relativistic charged particle with an arbitrary spin in central potential $e/r$ in terms of classical mechanics. We show that the spin-orbital interaction causes the precession of the plane of orbit around the vector of total angular momentum. The angular velocity of precession depends on the distance of the particle from the center. The effective potential for in-plane motion is central, with the corrections to Coulomb terms coming from spin-orbital interaction. The possible orbits of a quantum particle are determined by the Bohr-Sommerfeld quantization rule. We give examples of orbits corresponding to small quantum numbers, which were obtained by numerical integration of equations of motion. The energies of stationary states are determined by spin-orbital interaction.

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