Commutation Methods for Schroedinger Operators with Strongly Singular Potentials

TL;DR

This paper investigates the relationships between singular Weyl-Titchmarsh theory and commutation methods for Schrödinger operators with singular potentials, providing explicit formulas and applications to Bessel operators.

Contribution

It introduces new connections between Weyl-Titchmarsh theory and commutation methods, including explicit computation of Weyl functions for commuted operators.

Findings

Derived formulas for singular Weyl functions of commuted operators

Applied results to spherical Schrödinger (Bessel) operators

Explored links with Bäcklund-Darboux transformations

Abstract

We explore the connections between singular Weyl-Titchmarsh theory and the single and double commutation methods. In particular, we compute the singular Weyl function of the commuted operators in terms of the original operator. We apply the results to spherical Schroedinger operators (also known as Bessel operators). We also investigate the connections with the generalized Baecklund-Darboux transformation.