Trace formulas for Schr dinger operators on the half-line

We study the scattering problem for the Schr dinger equation on the half-line with the 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.