Atsuhide Ishida (Tokyo University of Science): On inverse scattering for N-body time-dependent harmonic oscillators

We consider an inverse scattering problem for an N-body quantum system with a time-dependent harmonic potential. Using the Enss-Weder time-dependent method, we prove that the scattering operator uniquely determines all pairwise interaction potentials. The proof is based on high-velocity estimates and a reduction of the N-body problem to suitable two-body channels.