A bound for ratios of eigenvalues of Schrodinger operators on the real line
Miklós Horváth Márton Kiss
Conference Publications 2005, 2005(Special): 403-409 doi: 10.3934/proc.2005.2005.403
We give upper estimates of ratios of eigenvalues of Schrödinger operators with nonnegative single-well potentials tending to infinity for large $|x|$, corresponding to previous estimates on a finite interval.
keywords: Schrodinger operator eigenvalues.
Spectral shift functions in the fixed energy inverse scattering
Miklós Horváth
Inverse Problems & Imaging 2011, 5(4): 843-858 doi: 10.3934/ipi.2011.5.843
In this paper the notion of the Krein spectral shift function is extended to the radial Schrödinger operator with fixed energy. Then we analyze the connections between the tail of the potential and the decay rate of the fixed-energy phase shifts. Finally we extend former results on the uniqueness of the fixed-energy inverse scattering problem to a general class of potentials.
keywords: estimations for Bessel functions. Inverse scattering with fixed energy Krein spectral shift function

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