Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensions

TL;DR

This paper provides explicit formulas and proves global uniqueness for solving the phaseless inverse scattering problem for the Schrödinger equation in multiple dimensions, using high-energy data.

Contribution

It introduces explicit solution formulas and establishes a global uniqueness result for the multidimensional phaseless inverse scattering problem.

Findings

Explicit formulas for the inverse scattering problem at high energies.

Global uniqueness of the solution with fixed energy data.

Applicable to Schrödinger equations with compactly supported potentials.

Abstract

We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we give also a global uniqueness result for this problem with appropriate data on a fixed energy neighborhood.