Article

**Inverse Problems 26, 105013, 14pp (2010)**[DOI: 10.1088/0266-5611/26/10/105013]

## Inverse Eigenvalue Problems for Perturbed Spherical Schrödinger Operators

### Aleksey Kostenko, Alexander Sakhnovich, and Gerald Teschl

We investigate the eigenvalues of perturbed spherical Schrödinger operators under the
assumption that the perturbation

*q(x)*satisfies*x q(x) ∈ L*. We show that the square roots of eigenvalues are given by the square roots of the unperturbed eigenvalues up to an decaying error depending on the behavior of^{1}(0,1)*q(x)*near*x=0*. Furthermore, we provide sets of spectral data which uniquely determine*q(x)*.
** MSC2000:** Primary 34B20, 34L15; Secondary 81V45 , 47A10

**Keywords:** *Schrödinger operators, spectral theory, strongly singular potentials*

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