Quantum scattering theory and applications

Abstract

Scattering theory provides a convenient framework for the solution of a variety of problems. In this thesis we focus on the combination of boundary conditions and scattering potentials and the combination of non-overlapping scattering potentials within the context of scattering theory. Using a scattering t-matrix approach, we derive a useful relationship between the scattering t-matrix of the scattering potential and the Green function of the boundary, and the t-matrix of the combined system, effectively renormalizing the scattering t-matrix to account for the boundaries. In the case of the combination of scattering potentials, the combination of t-matrix operators is achieved via multiple scattering theory. We also derive methods, primarily for numerical use, for finding the Green function of arbitrarily shaped boundaries of various sorts. These methods can be applied to both open and closed systems. In this thesis, we consider single and multiple scatterers in two dimensional strips ...