Scattering and inverse scattering for multipoint potentials at high energies

TL;DR

This paper develops high-energy scattering and inverse scattering methods for Schrödinger equations with multipoint Bethe-Peierls-Thomas-Fermi potentials, including formulas analogous to classical scattering theory.

Contribution

It introduces new high-energy scattering and inverse scattering formulas for singular multipoint potentials, extending classical results to this setting.

Findings

Derived analogs of the Born-Faddeev formula for these potentials.

Established inverse scattering reconstructions at high energies.

Presented results on scattering solutions at high energies.

Abstract

We consider the Schr\"odinger equation with a multipoint potential of Bethe-Peierls-Thomas-Fermi type. For this singular potential, we develop scattering and inverse scattering at high energies. In particular, in this framework, our results include analogs of the "regular" Born-Faddeev formula for the scattering amplitude and analogs of related "regular" inverse scattering reconstructions at high energies. Related results for scattering solutions at high energies are also presented.