### 論文 "On multidimensional inverse scattering for Stark Hamiltonians" のアブストラクト

#### By Tadayoshi Adachi and Katsuhiro Maehara Journal of Mathematical Physics 48 (2007), 042101.

Based on the Enss-Weder time-dependent method, we study one of multidimensional inverse scattering problems for Stark Hamiltonians. We first show that when the space dimension is greater than or equal to two, the high velocity limit of the scattering operator determines uniquely the potential like $|x|^{-\gamma}$ with $\gamma>1/2$ which is short-range under the Stark effect. This is an improvement of previous results obtained by Weder and Nicoleau. Moreover, we prove that for a given long-range part of the potential under the Stark effect, the high velocity limit of the Dollard-type modified scattering operator determines uniquely the short-range part of the potential.