[en] We show the asymptotic completeness for two-body quantum systems in an external electric field asymptotically non-zero constant in time. One of the main ingredients of this paper is to give some propagation estimates for physical propagators generated by time-dependent Hamiltonians which govern the systems under consideration.

[en] We study one of the multidimensional inverse scattering problems for quantum systems in time-dependent electric fields E(t), which is represented as E₀(1 + |t|)^−μ with 0 ⩽ μ < 1, based on the Enss–Weder time-dependent method. We show that when the space dimension is greater than or equal to 2, the high velocity limit of the scattering operator determines uniquely the short-range part like |x|^−γ with γ > 1/(2 − μ) of the potential belonging to the class rather wider than the one given by Adachi, Kamada, Kazuno and Toratani. Our method can also improve previous results in the case where E(t) is periodic in t with non-zero mean E₀. (paper)

[en] Based on the Enss–Weder time-dependent method, we study one of the multidimensional inverse scattering problems for quantum systems in an external electric field asymptotically zero in time as E₀(1 + |t|)^−μ with 0 < μ < 1, where E₀ is a non-zero constant electric field. We show that when the space dimension is greater than or equal to 2, the high velocity limit of the scattering operator determines uniquely the short-range potential like |x|^−γ with γ > 1/(2 − μ). Moreover, we prove that the high velocity limit of any one of the Dollard-type modified scattering operators determines uniquely the total potential. Dedicated to the memory of Professor Tetsuro Miyakawa

[en] In the spectral and scattering theory for a Schrödinger operator with a time-periodic potential $H(t)=p^2/2+V(t,x)$, the Floquet Hamiltonian $K=-<!--\; ???\; -->i{\mathrm{\partial <!--\; ???\; -->}}_t+H(t)$ associated with H(t) plays an important role frequently, by virtue of the Howland–Yajima method. In this paper, we introduce a new conjugate operator for K in the standard Mourre theory, that is different from the one due to Yokoyama, in order to relax a certain smoothness condition on V.