In this Thesis the self-consistent computational methods are applied to the study of the optical properties of semiconductor nanostructures with one- and two-dimensional quantum confinements. At first, the self-consistent Schrödinger-Poisson system of equations is applied to the cylindrical core-shell structure with type II band alignment without direct Coulomb interaction between carriers. The electron and hole states and confining potential are obtained from a numerical solution of this system. The photoluminescence kinetics is theoretically analyzed, with the nanostructure size dispersion taken into account. The results are applied to the radiative recombination in the system of ZnTe/ZnSe stacked quantum dots. A good agreement with both continuous wave and time-resolved experimental observations is found. It is shown that size distribution results in the photoluminescence decay that has essentially non-exponential behavior even at the tail of the decay where the carrier lifetime is almost the same due to slowly changing overlap of the electron and hole wavefunctions. Also, a model situation applicable to colloidal core-shell nanowires is investigated and discussed.

With respect to the excitons in type I quantum wells, a new computationally efficient and flexible approach of calculating the characteristics of excitons, based on a self-consistent variational treatment of the electron-hole Coulomb interaction, is developed. In this approach, a system of self-consistent equations describing the motion of an electron-hole pair is derived. The motion in the growth direction of the quantum well is separated from the in-plane motion, but each of them occurs in modified potentials found self-consistently. This approach is applied to a shallow quantum well with the δ-potential profile, for which analytical expressions for the exciton binding energy and the ground state eigenfunctions are obtained, and to the quantum well with the square potential profile with several different well and barrier materials. The numerical results yield lower exciton binding energies in comparison to standard variational calculations, while the iterative scheme used to calculate the energies and respective wavefunctions is stable, rapidly convergent and requires reduced computational effort. Thus, the method can be an important computational tool in computing exciton characteristics in quantum wells exceeding currently existing approaches in accuracy and efficiency. The method can also be naturally generalized for quantum wires and dots.