Two-parametric $\delta'$-interactions: approximation by Schr\"odinger operators with localized rank-two perturbations

TL;DR

This paper develops a new approximation method for $ abla$-interactions using Schrödinger operators with localized rank-two perturbations, providing a more accurate representation of point interactions in quantum mechanics.

Contribution

It introduces a novel approximation scheme for $ abla$-interactions via Schrödinger operators with localized rank-two perturbations, including a new approximation for $ abla$-interactions.

Findings

Constructed a norm resolvent approximation for point interactions.

Provided a new approximation method for $ abla$-interactions.

Demonstrated the effectiveness of the approximation in quantum models.

Abstract

We construct a norm resolvent approximation to the family of point interactions $f(+0)=\alpha f(-0)+\beta f'(-0)$, $f'(+0)=\alpha^{-1}f'(-0)$ by Schr\"odinger operators with localized rank-two perturbations coupled with short range potentials. In particular, a new approximation to the $\delta'$-interactions is obtained.