Muhammad Usman (Imperial) - "Trace formulas for Schrödinger operators on the half-line and star graph"

Abstract

We first study the scattering problem for the Schrödinger 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. We further use the matrix valued Schrödinger operator on the half-line with self-adjoint boundary conditions at origin and deduce similar trace identities.