Scattering on the line with a transfer condition at the origin
We consider the scattering problem of Sturm-Liouville operator on the line with a point transfer condition at the origin. The condition at the origin is described by transfer matrix M.
We investigate both forward and inverse problems. In the forward problems the nature of the spectrum (finitely many, simple, negative eigenvalues) as well as conditions which characterise transfer conditions resulting in self-adjoint problem will be presented. For the inverse problems we will show that the transfer matrix can be reconstructed from the set of eigenvalues and the reflection coefficient.