  This paper addresses the scattering of a beam of charged particles by an
infinitely long magnetic string in the context of the hydrodynamical approach
to quantum mechanics. The scattering is qualitatively analyzed by two
approaches. In the first approach, the quantum flow is studied via a
one-parameter family of complex potentials. In the second approach, the
qualitative theory of planar differential equations is used to obtain a
one-parameter family of Hamiltonian functions which determine the phase
portraits of the systems.
