dorsal/arxiv
View SchemaSpin 1/2 Particle on a Cylinder with Radial Magnetic Field
| Authors | C. Chryssomalakos, A. Franco, A. Reyes-Coronado |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212054 |
| URL | https://arxiv.org/abs/quant-ph/0212054 |
Abstract
We study the motion of a charged quantum particle, constrained on the surface of a cylinder, in the presence of a radial magnetic field. When the spin of the particle is neglected, the system essentially reduces to an infinite family of simple harmonic oscillators, equally spaced along the axis of the cylinder. Interestingly enough, it can be used as a quantum Fourier transformer, with convenient visual output. When the spin 1/2 of the particle is taken into account, a non-conventional perturbative analysis results in a recursive closed form for the corrections to the energy and the wavefunction, for all eigenstates, to all orders in the magnetic moment of the particle. A simple two-state system is also presented, the time evolution of which involves an approximate precession of the spin perpendicularly to the magnetic field. A number of plots highlight the findings while several three-dimensional animations have been made available on the web.
{
"annotation_id": "c73952c7-a004-4cf2-98f4-d004dbfb1ffb",
"date_created": "2026-03-02T18:01:56.665000Z",
"date_modified": "2026-03-02T18:01:56.665000Z",
"file_hash": "a1f02d1327c33d2471068a381634b5665aab859e5b6f6ab1b36c2bd0dee07cbf",
"private": false,
"record": {
"abstract": "We study the motion of a charged quantum particle, constrained on the surface\nof a cylinder, in the presence of a radial magnetic field. When the spin of the\nparticle is neglected, the system essentially reduces to an infinite family of\nsimple harmonic oscillators, equally spaced along the axis of the cylinder.\nInterestingly enough, it can be used as a quantum Fourier transformer, with\nconvenient visual output. When the spin 1/2 of the particle is taken into\naccount, a non-conventional perturbative analysis results in a recursive closed\nform for the corrections to the energy and the wavefunction, for all\neigenstates, to all orders in the magnetic moment of the particle. A simple\ntwo-state system is also presented, the time evolution of which involves an\napproximate precession of the spin perpendicularly to the magnetic field. A\nnumber of plots highlight the findings while several three-dimensional\nanimations have been made available on the web.",
"arxiv_id": "quant-ph/0212054",
"authors": [
"C. Chryssomalakos",
"A. Franco",
"A. Reyes-Coronado"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"physics.ed-ph"
],
"title": "Spin 1/2 Particle on a Cylinder with Radial Magnetic Field",
"url": "https://arxiv.org/abs/quant-ph/0212054"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "9f46e9cc-d7f7-4d13-958f-1a1e0f95f2e7",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}