Lippmann-Schwinger equation approach to scattering in quantum wires

We apply the Lippmann‐Schwinger equation for obtaining the scattering amplitudes and conductance as a function of Fermi energy for electrons scattering from one and two point defects in a two‐dimensional quantum wire. Further, we discuss the first and higher‐order Born approximation to the scattering wave function and show that keeping five terms in the Born series can lead to a convergent wave function (except for Fermi energy close to the subband energy where it naturally diverges). It has been stated previously that electron transmission through a single point defect in a quantum wire is perfect at every subband minima independent of where the scatterer is located. However, here we demonstrate that perfect transmission at subband minima is strongly affected by the transversal position of the defect. In particular, we show that the perfect transparency effect is modified when the scatterer is located at the nodes of a normal confinement mode.