  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.
