Schroedinger operators with singularly scaled magnetic and electric potentials

TL;DR

This paper investigates the behavior of one-dimensional Schrödinger operators with highly localized magnetic and electric potentials, focusing on their norm resolvent convergence as the potentials become increasingly singular.

Contribution

It provides new insights into the limiting behavior of Schrödinger operators with singularly scaled potentials, expanding understanding of their spectral properties.

Findings

Established conditions for norm resolvent convergence

Characterized the limiting operators with singular potentials

Extended previous results to magnetic and electric cases

Abstract

The norm resolvent convergence of a family of one-dimensional Schroedinger operators with singular magnetic and electric potentials of small support is studied.