Resonances in a two-dimensional electron waveguide with a single δ -function scatterer

We study the conductance properties of a straight two-dimensional electron waveguide with an s-like scatterer modeled by a single δ-function potential with a finite number of modes. Even such a simple system exhibits interesting resonance phenomena. These resonances are explained in terms of quasibound states both by using a direct solution of the Schr\"odinger equation and by studying the Green's function of the system. Using the Green's function we calculate the survival probability as well as the power absorption, and show the influence of the quasibound states on these two quantities.