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

We study the conductance properties of a straight two-dimensional electron waveguide with an s-like scatterer modeled by a single delta-function potential with a finite number of modes. Even such a simple system exhibits interesting resonance phenomena. These resonances are explained in terms of quasi-bound states both by using a direct solution of the Schroedinger 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 quasi-bound states on these two quantities.