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Inverse scattering theory and trace formulae for one-dimensional Schrödinger problems with singular potentials (1503.01276v2)
Published 4 Mar 2015 in math-ph, cond-mat.soft, cond-mat.stat-mech, hep-th, and math.MP
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.