1-D Schr\"odinger operators with local point interactions: a review

TL;DR

This paper reviews recent advances in the theory of one-dimensional Schrödinger operators with local point interactions, highlighting developments driven by extension theory of symmetric operators and differential operators with distributional coefficients.

Contribution

It provides a comprehensive overview of recent theoretical progress in modeling 1-D Schrödinger operators with point interactions on discrete sets.

Findings

Enhanced understanding of extension theory applications

New classifications of point interactions

Connections between differential operators and distributional coefficients

Abstract

We review recent developments in the theory of 1-D Schr\"odinger operators with local point interactions on a discrete set. The progress in this area was stimulated by recent advances in the extension theory of symmetric operators and in the theory of ordinary differential operators with distributional coefficients.