Article

**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*

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