AG Mathematische Physik, Gerardo Franco Cordova: Analytic Properties of the Scattering Matrix of Discrete Schrödinger Operators

Gerardo Franco Cordova

Analytic Properties of the Scattering Matrix of Discrete Schrödinger

Operators

Abstract:
We develop a scattering theory for discrete Schrödinger operators. We

represent the scattering matrix in terms of special solutions to the

eigenvalue equation, known as Jost solutions. This representation

facilitates the analytic extension of certain coefficients of the

scattering matrix, enabling a detailed study of their analytic

properties. Furthermore, we connect these analytic properties of the

scattering matrix to the spectral properties of the Hamiltonian,

ultimately deriving a version of the Levinson formula.