An inverse scattering problem with the Aharonov–Bohm effect

A direct and an inverse scattering method is developed for Schrödinger operators with electromagnetic fields in the case of obstacles in order to study the well-known Aharonov–Bohm effect. In dimension greater or equal to three, we show that the electric potential and the magnetic field are uniquely determined by the S-operator. In the two-dimensional case, some obstruction appears based on a quantification of the magnetic flux.