Atsuhide Ishida (Tokyo University of Science): On Inverse Scattering for N-body Time-dependent Harmonic Oscillators

Abstract: 

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.