### 論文
"Scattering theory for two-body quantum systems with singular potentials in a time-periodic electric field"
のアブストラクト

#### By Tadayoshi Adachi, Toshiyuki Kimura and Yoshimasa Shimizu

Journal of Mathematical Physics **51** (2010), 032103.

Recently the first author has proved
the asymptotic completeness for $N$-body
quantum systems with long-range interactions in a time-periodic
electric field whose mean in time is nonzero by obtaining propagation
estimates for the physical propagator. However, in his work,
it is needed that potentials under consideration are
sufficiently smooth. In this paper, when $N=2$,
we prove the asymptotic completeness of (modified) wave
operators under the assumption that
the potential has the local singularity
of type $|x|^{-1+\epsilon}$
when $d\ge3$ and $0<\epsilon<1$,
where $d$ is the space dimension.
We also discuss the modifiers in the position representation,
which are used in the definition of modified wave operators
in the long-range case.

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