In this paper some advancements in the development of the Wigner-function approach to quantum electron transport are presented. In particular we reexamined the problem of the interaction of the carriers with a potential profile with the purpose of isolating relevant differences with respect to classical dynamics. In order to simplify the notation phonon scattering has not been included. In particular, two cases are considered: (1) infinite potential barriers, and (2) the separation of the classical force from the quantum contributions in a general potential profile.