The Density-Gradient Correction as a Disguised Pilot Wave of de Broglie

Abstract

Recent papers on advanced semiconductor devices adopt a model called density-gradient correction, in which the standard electric potential acting on the carriers is modified by a non-linear term involving the carrier concentration and its second derivatives. When applied to cases where quantum effects are not negligible, the modified model improves the results with respect to the standard approach. The paper shows how, starting from a straightforward derivation of the density-gradient correction from the Schrödinger equation, its interpretation as an addition to the potential energy is questionable, and makes a few considerations for further investigation on the subject.