Inverse scattering for $N$-body time-decaying harmonic oscillators

Abstract

In the previous study (Ishida, 2025), the author proved the uniqueness of short-range potential functions using the Enss-Weder time-dependent method (Enss and Weder, 1995) for a two-body quantum system described by time-decaying harmonic oscillators. In this study, we extend the result of Ishida (2025) to the $N$-body case. We use the approaches developed in Enss and Weder (1995), Weder (1996), and Valencia and Weder (2012) to prove that the high-velocity limit of the scattering operator uniquely determines all the pairwise interaction potentials among the $N$ particles, focusing respectively on each fixed pair of particles.