Computing the electronic properties of solid-states at the quantum mechanical level can be time-consuming, especially for realistic systems, e.g. semiconducting nanowires or van der Waals heterostructures, as large matrices must be diagonalized. Different numerical methods have been developed over the past decades to speed up such computations. Recently, techniques using randomization have been proposed to achieve this goal, typically by projecting the matrix of interest on a randomly chosen low-dimensional subspace. By doing so, the problem size is reduced and consequently, the computational overhead as well. In this presentation, we revisit such randomization methods and discuss their convergence and approximation guarantees. Improvements relying on recent advances in the random projections literature are also suggested. In addition to the theoretical discussion, we present numerical experiments for a so-called memristor structure whose charge density is approximated with the proposed technique. We show convergence and approximation errors and discuss the general applicability and limitations of randomization methods.