Past studies have mostly treated the case of nanocrystals from group III-V and II-VI semiconductors. With the k · p approach, the noninteracting single-particle picture has been discussed. Later on, the Coulomb interaction was treated by using the noninteracting particle wave function. Regardingperovskites, the band structure in the bulk has been investigated via the use of density functional theory. Less work was done on the calculations ofperovskite nanocrystals. Becker et al. have discussed the correlated single exciton in perovskite nanocrystals. So far, all of the theoretical studies on perovskite nanocrystals have not focused on the properties of any electron-hole system other than a single exciton. However, with increasing excitation power, more than one pair of electron and hole can be created inside a nanocrystal. The radiative lifetime of an exciton in its ground state falls in the sub-nanosecond range for perovskites, which seems to be similar to that of GaAs and is notably shorter than in many other semiconductors such as CdSe or CuCl. The fast radiative decay might be linked to the brightness of these perovskite nanocrystals. The recorded one-photon absorption cross-section is also quite good compared to the nanocrystals of other materials of the same size. This fact partially explains why perovskites are generally good light absorbers for solar cells.In Chapter 2, we start the technical discussion with a quick recapitulation of the band structure calculations. The k · p Hamiltonian is viewed as a way to model the kinetic energy at the band edge of the semiconductor. To further boost the computational efficiency, we make the assumption of spherical symmetry for the band structure as well as the confining potential. By setting the Kane parameter Ep = 0 in the k · p model, we recover the effective mass model (parabolic approximation).In Chapter 3, we present the Hartree-Fock formulation as a mean-field level approximation to the exact intercarrier Coulomb interaction. As an application, the calculated single exciton energy will be compared to experimental figures at the end of this chapter. The Hartree-Fock approximation shows to be a reasonable description for a single exciton binding energy in perovskites, see the results of Section 3.4.Chapter 4 is concerned with the theoretical foundation for obtaining the trion and biexciton shifts. There, we use the second-order many-body perturbation theory approach to clearly demonstrate that some nonzero red-shifts are present for trions as well as the biexciton. The quantitative prediction is less than satisfactory at second-order level, which implies that an all-order method is needed for a better comparison with experiments. To complete the discussion of many-body perturbation theory, we shall apply the second-order degenerate version to calculate the long-range exchange contribution to the dark-bright exciton energy splitting.Chapter 5 deals with the electron-photon interaction. At Hartree-Fock level, the computed radiative decay rate and one-photon absorption cross-section turn out to be too small compared to the measured values. The electron-hole correlation in the many-body approach greatly improves the theoretical prediction of these quantities, bridging the gap between our theory and the experiments. We conclude that the Coulomb correlation also plays a very important role in the electron-photon interaction. Again, to have a good quantitative agreement with the measurements, this correlation must be included up to all orders. Even though the variational method can take care of the Coulomb interaction nonperturbatively in principle, it becomes increasingly involved for the calculations of the higher exciton states. We remark that our current approach requires the same level of complexity when applied to these excited states, which is beneficial for correcting the whole absorption spectrum.