Trace formulas for Schrödinger operators on the half-line

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.

20 pages