Trace formulas for Schrödinger operators on the half-line

2011/09/05 by Semra Demirel, Muhammad Usman, Demirel, Semra +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP

paper · pdf · doi:10.48550/arxiv.1109.1024

20 pages

arxiv created 2011/09/05 · arxiv updated 2011/09/07

Abstract

We study the scattering problem for the Schrödinger equation on the half-line with Robin boundary condition at the origin. We derive an expression for the trace of the difference of the perturbed and unperturbed resolvent in terms of a Wronskian. This leads to a representation for the perturbation determinant and to trace identities of Buslaev-Faddeev type.

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