Equivalence of wave function matching and Green's functions methods for quantum transport: generalized Fisher-Lee relation.

We present a proof of an exact equivalence of the two approaches that are most used in computing conductance in quantum electron and phonon transport: the wave function matching and Green's functions methods. We can obtain all the quantities defined in one method starting from those obtained in the other. This completes and illuminates the work started by Ando (19918017) and continued later by Khomyakov(2005035450).