On real resonances for three-dimensional Schr\"odinger operators with point interactions

TL;DR

This paper proves that Schr"odinger operators with finitely many point interactions in three dimensions do not have positive real resonances, impacting the understanding of their scattering and dispersive properties.

Contribution

It establishes the absence of positive real resonances for a class of Schr"odinger operators with point interactions in three dimensions, a novel result in scattering theory.

Findings

No positive real resonances for the considered operators

Insights into dispersive and scattering behavior of these operators

Enhanced understanding of spectral properties of point interaction Schr"odinger operators

Abstract

We prove the absence of positive real resonances for Schr\"odinger operators with finitely many point interactions in $\mathbb{R}^3$ and we discuss such a property from the perspective of dispersive and scattering features of the associated Schr\"odinger propagator.