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Article . 2023 . Peer-reviewed
License: CC BY
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Article . 2023
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https://dx.doi.org/10.48550/ar...
Article . 2023
License: arXiv Non-Exclusive Distribution
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Coulomb Problem for Classical Spinning Particles

Authors: Dmitry S. Kaparulin; Nikita A. Sinelnikov;

Coulomb Problem for Classical Spinning Particles

Abstract

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.

Country
Russian Federation
Related Organizations
Keywords

High Energy Physics - Theory, Quantum Physics, кулоновская задача, Elementary particle physics, FOS: Physical sciences, релятивистское движение, QC793-793.5, coulomb problem, spin, High Energy Physics - Theory (hep-th), Бора-Зоммерфельд квантование, spinning particle, Bohr–Sommerfeld quantization, Quantum Physics (quant-ph), заряженные частицы

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    3
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green
gold