Quantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensions

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 $q\Phi /2\pi \hslash c$ takes integers or half integers. In both cases the cross sections obtained are rather different from that for pure Coulomb scattering.

12 pages, REVTeX, no figure

Cited by in corpus (4)

• Scattering of relativistic particles by a Coulomb field in two dimensions
• Semiclassical Quantization for the Spherically Symmetric Systems under an Aharonov-Bohm magnetic flux
• Scattering of relativistic particles with Aharonov-Bohm-Coulomb interaction in two dimensions
• On the partial wave amplitude of Coulomb scattering in three dimensions