Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators

Details Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators

2010-04-23

arxiv.org/abs/1004.4175v2

Inverse Problems 26, 105013 (2010)

Mathematics

Spectral Theory

14 pages

Scientific paper

10.1088/0266-5611/26/10/105013

We investigate the eigenvalues of perturbed spherical Schr\"odinger operators under the assumption that the perturbation $q(x)$ satisfies $x q(x) \in L^1(0,1)$. 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 $q(x)$ near $x=0$. Furthermore, we provide sets of spectral data which uniquely determine $q(x)$.

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