dorsal/arxiv
View SchemaQuantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensions
| Authors | Qiong-gui Lin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9905019 |
| URL | https://arxiv.org/abs/quant-ph/9905019 |
| DOI | 10.1103/PhysRevA.59.3228 |
| Journal | Phys.Rev. A59 (1999) 3228-3235 |
Abstract
We propose a simple quantum mechanical equation for $n$ particles in two dimensions, each particle carrying electric charge and magnetic flux. Such particles appear in (2+1)-dimensional Chern-Simons field theories as charged vortex soliton solutions, where the ratio of charge to flux is a constant independent of the specific solution. As an approximation, the charge-flux interaction is described here by the Aharonov-Bohm potential, and the charge-charge interaction by the Coulomb one. The equation for two particles, one with charge and flux ($q, \Phi/Z$) and the other with ($-Zq, -\Phi$) where $Z$ is a pure number is studied in detail. The bound state problem is solved exactly for arbitrary $q$ and $\Phi$ when $Z>0$. The scattering problem is exactly solved in parabolic coordinates in special cases when $q\Phi/2\pi\hbar c$ takes integers or half integers. In both cases the cross sections obtained are rather different from that for pure Coulomb scattering.
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"abstract": "We propose a simple quantum mechanical equation for $n$ particles in two\ndimensions, each particle carrying electric charge and magnetic flux. Such\nparticles appear in (2+1)-dimensional Chern-Simons field theories as charged\nvortex soliton solutions, where the ratio of charge to flux is a constant\nindependent of the specific solution. As an approximation, the charge-flux\ninteraction is described here by the Aharonov-Bohm potential, and the\ncharge-charge interaction by the Coulomb one. The equation for two particles,\none with charge and flux ($q, \\Phi/Z$) and the other with ($-Zq, -\\Phi$) where\n$Z$ is a pure number is studied in detail. The bound state problem is solved\nexactly for arbitrary $q$ and $\\Phi$ when $Z\u003e0$. The scattering problem is\nexactly solved in parabolic coordinates in special cases when $q\\Phi/2\\pi\\hbar\nc$ takes integers or half integers. In both cases the cross sections obtained\nare rather different from that for pure Coulomb scattering.",
"arxiv_id": "quant-ph/9905019",
"authors": [
"Qiong-gui Lin"
],
"categories": [
"quant-ph",
"hep-th"
],
"doi": "10.1103/PhysRevA.59.3228",
"journal_ref": "Phys.Rev. A59 (1999) 3228-3235",
"title": "Quantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensions",
"url": "https://arxiv.org/abs/quant-ph/9905019"
},
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