Zero resonances for localised potentials

TL;DR

This paper studies Hamiltonians with localized potentials, providing a variational method to identify resonant coupling parameters, and applies this to calculate the first resonance for Yukawa potentials in three dimensions.

Contribution

It introduces a variational characterization of resonant parameters and offers a constructive approach for Yukawa potentials in three-dimensional space.

Findings

Derived bounds for resonant free regions.

Provided a method to estimate the first resonant parameter.

Applied the approach specifically to Yukawa potentials.

Abstract

This paper considers Hamiltonians with localised potentials and gives a variational characterisation of resonant coupling parameters, which allow to provide estimates for the first resonant parameter and in turn also to provide bounds for resonant free regions. As application we provide a constructive approach to calculate the first resonant parameter for Yukawa type potentials in $\mathbb R^3$.