An inverse scattering problem with the Aharonov-Bohm effect

A direct and an inverse scattering method is developed for Schrodinger oper ators with electromagnetic fields in the case of obstacles in order to stud y the well-known Aharonov-Bohm effect. In dimension greater or equal to thr ee, we show that the electric potential and the magnetic field are uniquely determined by the S-operator. In the two-dimensional case, some obstructio n appears based on a quantification of the magnetic flux. (C) 2000 American Institute of Physics. [S0022-2488(00)03507-6].