Determining metrics from the scattering map of the time-dependent Schrödinger equation

Abstract

For a time dependent Schrödinger equation, the scattering map is the map sending the asymptotic profile of solution as $t\to -\infty$ to its asymptotic profile as $t\to +\infty$. In this paper we show that, for certain class of metrics, the scattering maps associated to two Schrödinger operators with two time dependent metrics only differ by a compact operator if and only if these two metrics are related by a pull-back of a diffeomorphism.

arXiv admin note: text overlap with arXiv:2601.20225