Inverse scattering problem with part of the fixed-energy phase shifts

TL;DR

This paper investigates the inverse scattering problem at fixed energy, identifying which subsets of phase shifts enable unique reconstruction of a compactly supported potential, with specific emphasis on even angular momenta.

Contribution

It demonstrates that certain subsets of phase shifts, such as all even angular momenta, are sufficient for unique potential recovery in inverse scattering.

Findings

Knowledge of all even angular momentum phase shifts suffices for unique potential reconstruction.

Part of the fixed-energy phase shifts can determine the potential uniquely.

The study clarifies conditions for unique inverse scattering solutions.

Abstract

It is found what part of the fixed-energy phase shifts allows one to recover uniquely a compactly supported potential. For example, the knowledge of all phase shifts with even angular momenta is sufficient to recover the above potential.