Spectral Asymptotics for Perturbed Spherical Schr\"odinger Operators and Applications to Quantum Scattering

TL;DR

This paper derives high energy asymptotics for spectral functions of perturbed spherical Schrödinger operators and applies these results to improve inverse spectral theorems and uniqueness in quantum scattering with angular momentum.

Contribution

It provides new high energy asymptotic formulas for spectral measures of Bessel operators and enhances inverse spectral and scattering theory results.

Findings

High energy asymptotics for spectral measures derived

Improved local Borg-Marchenko theorem established

Uniqueness results for radial quantum scattering proven

Abstract

We find the high energy asymptotics for the singular Weyl--Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schr\"odinger operators (also known as Bessel operators). We apply this result to establish an improved local Borg-Marchenko theorem for Bessel operators as well as uniqueness theorems for the radial quantum scattering problem with nontrivial angular momentum.