The Friedel formula describing oscillations of the electron density due to the presence of a single impurity has been known for a long time. Here, we derive a generalized formula for the case of many impurities and we discuss in detail specific cases where few scattering centers are present. Interference patterns in the density oscillations are shown. The arguments are presented when the standard Friedel’s formula can be used additively and the inter impurity scatterings might be neglected. One can view our result as the Huygens principle applied to Friedel oscillations in many impurity cases. Abstract Published by the Jagiellonian University 2026 authors
Skolimowski et al. (Fri,) studied this question.