Coulomb Problem for Classical Spinning Particles

We consider the 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...

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Bibliographic Details
Published in:Universe (Basel) 2023-05, Vol.9 (5), p.219
Main Authors: Kaparulin, Dmitry S., Sinelnikov, Nikita A.
Format: Article
Language:English
Subjects:
Angular momentum
Bohr–Sommerfeld quantization
Charged particles
coulomb problem
Electromagnetism
Energy
Equations of motion
Orbits
Quantum field theory
Quantum physics
spin
spinning particle
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Summary:We consider the 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 centre. 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.
ISSN:2218-1997
2218-1997
DOI:10.3390/universe9050219