The spatial and time dependencies of the dielectric function for the quasi-two dimensional (Q2D) electron gas (EG) in a finite confining potential quantum well (QW) are calculated by using a self-consistent approach (SQF). Taking into account the influences of mismatch of strong discontinuous dielectric constant and effective masse across the interfaces the dielectric response function analytic expressions are derived for a rectangular finite potential barrier QW for the first time. The deviations from the results when these mismatches are absent are established. By using exactly calculated dielectric function a comparison with the respective asymptotic expressions of finite and infinite confining models is presented both analytically and numerically on the base of realistic EuS/PbS/EuS QW. The transition interval between 2D and 3D cases has been demonstrated numerically.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.