3 research outputs found
Quantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensions
We propose a simple quantum mechanical equation for 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 () and the other with () where
is a pure number is studied in detail. The bound state problem is solved
exactly for arbitrary and when . The scattering problem is
exactly solved in parabolic coordinates in special cases when takes integers or half integers. In both cases the cross sections obtained
are rather different from that for pure Coulomb scattering.Comment: 12 pages, REVTeX, no figur