Commun. Math. Phys. 322, 255-275 (2013) [DOI: 10.1007/s00220-013-1698-x]

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

Aleksey Kostenko and Gerald Teschl

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.

MSC2000: Primary 34B20, 34L25; Secondary 34L05, 47A10
Keywords: Schrödinger operators, spectral theory, strongly singular potentials, scattering theory

TeX file (60K) or pdf file (363K)