Modeling conduction in electron waveguides with finite-range impurities

We study the conductance of an electron waveguide with a finite range impurity using reaction matrix theory. We compute the scattering matrix for the waveguide and use it to obtain an exact expression for the Landauer conductance. In an effort to simplify the computation of conductance in such systems, we review the convergence difficulties that occur if δ-function impurities in two space dimensions are used in place of finite range impurities. We compare our exact result for the waveguide conductance with a finite range impurity with the case of the δ-function impurity with the finite number of modes. We determine conditions for which a δ-function impurity can be used to approximate the conductance when a finite range impurity is present.