The Aharonov-Bohm Effect: Mathematical Aspects of the Quantum Flow

This paper addresses the scattering of a beam of charged particles by an infinitely long magnetic string in the context of the hydrodynam-ical 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 sec-ond 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