Inverse scattering in the Stark effect. (13th September 2019) - Ishida, Atsuhide
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 (1995 J. Math. Phys .36 3902–21), we prove that the high-velocity limit of the scattering operator uniquely determines 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 uniquely determines 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 (2007 J. Math. Phys .48 042101; Adachi et al 2013 Inverse Problems 29 085012).