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.
Related papers
- The Kepler problem on the lattice [0.0]
We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential.
We demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice.
arXiv Detail & Related papers (2024-06-26T23:16:35Z) - The quantum Hall effect under the influence of gravity and inertia: A
unified approach [44.99833362998488]
We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia.
The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained.
arXiv Detail & Related papers (2024-03-11T18:01:55Z) - Coherent transfer of the transverse momentum of an optical vortex beam
to the motion of a single trapped ion [22.42090005507693]
We demonstrate the excitation, using a structured light beam carrying orbital angular momentum, of the center of mass motion of a single atom.
We characterize the coherent interaction by an effective transverse Lamb-Dicke factor $etamathrmexp_perp62(5)$ which is in agreement with our theoretical prediction $etamathrmtheo_perp57(1)$
arXiv Detail & Related papers (2022-06-10T06:15:08Z) - Effect of Wigner rotation on estimating unitary-shift parameter of
relativistic spin-1/2 particle [21.22196305592545]
We use a specific model of a relativistic spin-1/2 particle described by a gaussian wave function with a spin down in the rest frame.
It is shown that estimation accuracy decreases monotonically in the velocity of the observer when the moving observer does not measure the spin degree of freedom.
arXiv Detail & Related papers (2022-04-21T20:26:45Z) - Relativistic Mechanics Theory for Electrons that Exhibits Spin,
Zitterbewegung, Superposition and Produces Dirac's Wave Equation [0.0]
The spin of an electron is a natural part of its space-time path as a point particle.
The total motion can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called the spin center.
arXiv Detail & Related papers (2021-08-14T02:45:03Z) - Motion-induced radiation due to an atom in the presence of a graphene
plane [62.997667081978825]
We study the motion-induced radiation due to the non-relativistic motion of an atom in the presence of a static graphene plate.
We show that the effect of the plate is to increase the probability of emission when the atom is near the plate and oscillates along a direction perpendicular to it.
arXiv Detail & Related papers (2021-04-15T14:15:23Z) - Zitterbewegung of massless particles [91.3755431537592]
Zitterbewegung of massless particles with an arbitrary spin is analyzed in various representations.
Zitterbewegung takes place in any representation except for the Foldy-Wouthuysen one.
arXiv Detail & Related papers (2020-08-12T14:16:44Z) - Twisting Neutral Particles with Electric Fields [0.0]
We show that spin-orbit coupled states are generated in neutral magnetic spin 1/2 particles travelling through an electric field.
We propose a neutron optical experiment to measure the transverse effect.
arXiv Detail & Related papers (2020-07-07T11:18:56Z) - Quantum walk on a graph of spins: magnetism and entanglement [0.0]
We introduce a model of a quantum walk on a graph in which a particle jumps between neighboring nodes and interacts with independent spins sitting on the edges.
Entanglement propagates with the walker.
We apply this model to the case of a one dimensional lattice, to investigate its magnetic and entanglement properties.
arXiv Detail & Related papers (2020-06-26T09:32:57Z) - Position and spin in relativistic quantum mechanics [68.8204255655161]
The position and spin operators in the Foldy-Wouthuysen representation are quantum-mechanical counterparts of the classical position and spin variables.
The spin-orbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the rest-frame spin are used.
arXiv Detail & Related papers (2020-03-14T07:49:40Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.