Point interaction in dimension two and three as models of small scatterers

TL;DR

This paper demonstrates that point interactions in two and three dimensions can effectively model scattering on localized potentials, including both attractive and repulsive types, within a specific energy range.

Contribution

It introduces a framework showing point interactions as models for localized potential scattering in 2D and 3D, expanding their applicability.

Findings

Point interactions can model scattering on localized potentials.

Both attractive and repulsive potentials are included.

The models are valid within a specific energy range.

Abstract

In addition to the conventional renormalized--coupling--constant picture, point interactions in dimension two and three are shown to model within a suitable energy range scattering on localized potentials, both attractive and repulsive.