### 論文
"On multidimensional inverse scattering in an external electric field asymptotically zero in time"
のアブストラクト

#### By Tadayoshi Adachi, Tatsuya Kamada, Masayuki Kazuno and Keisuke Toratani

Inverse Problems 27 (2011), 065006.

Based on the Enss-Weder time-dependent method, we study one of multidimensional inverse scattering problems for quantum systems in an external electric field asymptotically zero in time as $E_0(1+|t|)^{-\mu}$ with $0<\mu<1$, where $E_0$ is a non-zero constant electric field. We show that when the space dimension is greater than or equal to two, the high velocity limit of the scattering operator determines uniquely the short-range potential like $|x|^{-\gamma}$ with $\gamma>1/(2-\mu)$. Moreover, we prove that the high velocity limit of any one of the Dollard-type modified scattering operators determines uniquely the total potential.

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