2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105408This paper develops a scattering theory to examine how point impurities affect transport through quantum wires. While some of our new results apply specifically to hard-walled wires, others--for example, an effective optical theorem for two-dimensional waveguides--are more general. We apply the method of images to the hard-walled guide, explicitly showing how scattering from an impurity affects the wire's conductance. We express the effective cross section of a confined scatterer entirely in terms of the empty waveguide's Green's function, suggesting a way in which to use semiclassical methods to understand transport properties of smooth wires. In addition to predicting some new phenomena, our approach provides a simple physical picture for previously observed effects such as conductance dips and confinement-induced resonances.19 pages, 8 figures. Accepted for publication in Physical Review B. Minor additions to text, added referencesQuantum PhysicsMesoscale and Nanoscale Physicstext