Quantum inverse scattering for time-decaying harmonic oscillators

Abstract: Different from the usual harmonic oscillator, the time-decaying harmonic oscillator accelerates particles and generates scattering states. We study one of the multidimensional inverse scatterings in this two-body quantum system perturbed by short-range potential functions that have a bounded part and a locally singular part. Applying the Enss--Weder time-dependent method, we prove that the scattering operator determines the potential functions uniquely.