Green's function methods in 1D nanoscale electron waveguides
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R-matrix theory has been used to analyze a variety of scattering potentials in ballistic electron waveguides. The S-matrix is the principal result of this method. Here we analyze ballistic electron scattering in a 1D waveguide with a step potential at its terminus using Green’s function theory. We calculate the S-matrix for this system, scattering particles’ quasibound states, and the survival probability of a particle initially localized in the step region. We then apply R-matrix theory to the same problem. In doing so, we demonstrate the versatility of the Green’s function approach, but also its relative complexity.