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arXiv · 1503.01276

Inverse scattering theory and trace formulae for one-dimensional Schr\"odinger problems with singular potentials

Sergei B. Rutkevich·H. W. Diehl
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Abstract

Inverse scattering theory is extended to one-dimensional Schr\"odinger problems with near-boundary singularities of the form $v(z\to 0)\simeq -z^{-2}/4+v_{-1}z^{-1}$. Trace formulae relating the boundary value $v_0$ of the nonsingular part of the potential to spectral data are derived. Their potential is illustrated by applying them to a number of Schr\"odinger problems with singular potentials.

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Sergei B. Rutkevich, H. W. Diehl. 2015-03-04. Inverse scattering theory and trace formulae for one-dimensional Schr\"odinger problems with singular potentials. https://doi.org/10.1088/1751-8113/48/37/375201

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