Inverse scattering in Stark effect

Abstract

We study one of the multidimensional inverse scattering problems for quantum systems governed by the Stark Hamiltonians. By applying the time-dependent method developed by Enss and Weder in 1995, we prove that the high-velocity limit of the scattering operator determines uniquely the short-range interaction potentials. Moreover, we prove that, when a long-range interaction potential is given, the high-velocity limit of the Dollard-type modified scattering operator determines uniquely the short-range part of the interactions. We allow the potential functions to belong to very broad classes. These results are improvements on the previous results obtained by Adachi and Maehara in 2007 and Adachi, Fujiwara, and Ishida in 2013.