Inverse scattering for $N$-body time-decaying harmonic oscillators
Mathematical Physics
2026-01-21 v4 Analysis of PDEs
math.MP
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 -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 particles, focusing respectively on each fixed pair of particles.
Cite
@article{arxiv.2510.04702,
title = {Inverse scattering for $N$-body time-decaying harmonic oscillators},
author = {Atsuhide Ishida},
journal= {arXiv preprint arXiv:2510.04702},
year = {2026}
}