This paper develops a scattering theory to examine how point impurities affect transport through quantum wires. While some of our 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.
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