Within the scheme of the large-scale atomic effective pseudopotential program (LATEPP), the Schrödinger equation of an electronic system is solved within an effective single-particle approach. Although not limited to, it focuses on the recently introduced atomic effective pseudopotentials derived from screened local effective crystal potentials as obtained from self-consistent density functional theory calculations. The problem can be solved in both real (real-space grid) and reciprocal space (plane-wave basis functions). Following the idea of atomic effective pseudopotentials, the density, and hence a self-consistent cycle, is not required and not implemented. An iterative solver is implemented to deliver the eigenstates close to a selected reference energy, e.g., around the band gap of a semiconductor. This approach is particularly well suited for theoretical investigations of the electronic structure of semiconductor nanostructures and we demonstrate linear scaling with the system size up to around 100000 atoms on a single standard compute node. Moreover, an efficient real-space treatment of spin-orbit coupling within the pseudopotential framework is proposed in this work allowing for a fully relativistic description.