Spectral Asymptotics for Perturbed Spherical Schrödinger Operators and Applications to Quantum Scattering

Abstract

We find the high energy asymptotics for the singular Weyl--Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schrödinger 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.

20 pages

References in corpus (3)

• On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators
• Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators
• Uniqueness Results for Schroedinger Operators on the Line with Purely Discrete Spectra

Cited by in corpus (8)

• Spectral asymptotics for canonical systems
• A transmutation operator method for solving the inverse quantum scattering problem
• Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators
• Dispersion Estimates for One-Dimensional Schrödinger Equations with Singular Potentials
• On Spectral Deformations and Singular Weyl Functions for One-Dimensional Dirac Operators
• Direct and inverse spectral theorems for a class of canonical systems with two singular endpoints
• Transformation operators for spherical Schrödinger operators
• Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions