One of the core concepts in nanoscience and nanotechnology is the bottom-up approach, taking electrons, atoms, or molecules as the building blocks from which to create man-made nanosystems with the specific and desired electronic, biological, material, mechanical, or environmental properties. This approach however, poses a new and fundamental scientific challenge: the mastering of the way in which electrons, atoms, or molecules interact which each other, governed by the non-intuitive laws of quantum mechanics. This challenge drives in turn the search for better and accurate calculation methods aimed to the prediction, with the largest reliability as possible, of the properties of a particular array of electrons or atoms (nano-design). The present research training project points towards the fulfilment of this goal: the development and application of Density Functional Theory (DFT) methods specially designed for the treatment of interacting strongly inhomogeneous electron gases as those formed in semiconductor quantum wells and dots. The research plan is divided in three parts: a) the static case without magnetic field, b) the static case with magnetic field, and c) the time-dependent case. In all cases, the so-called Optimized Effective Potential (orbital-based functionals) method of DFT will be the general framework of the calculations. While the utility of this method at the exchange level has been already demonstrated, its value at the correlation level still is an open question. The application of orbital-based functionals to the calculation of the electronic properties of quantum-confined systems is still in their infancy. The present project aims to contribute to close this gap, appealing to an almost ideal match between the expertise of Prof. Gross and their group in DFT with the candidate's ample expertise on the electronic structure of semiconductors.