Computing Scattering Resonances

TL;DR

This paper presents a universal, constructive algorithm for computing scattering resonances of Schrödinger operators that only requires knowledge of the potential's support size and its values at specific points.

Contribution

It introduces a novel, potential-independent method for computing scattering resonances with minimal prior information about the potential.

Findings

Algorithm works for any potential with known support size

Requires only potential values at requested points

Applicable to a wide class of Schrödinger operators

Abstract

The question of whether it is possible to compute scattering resonances of Schr\"odinger operators - independently of the particular potential - is addressed. A positive answer is given, and it is shown that the only information required to be known a priori is the size of the support of the potential. The potential itself is merely required to be $\mathcal{C}^1$. The proof is constructive, providing a universal algorithm which only needs to access the values of the potential at any requested point.