This work presents an analysis of the energy structure of carriers enclosed in self-assembled InAs quantum dots. Capacitance-voltage-spectroscopy (CV) with perpendicular magnetic fields is used to identify the energy structure of holes in quantum dots. Applying a two-dimensional harmonic oscillator model, we demonstrate an irregular filling sequence where the d states are occupied with holes before the filling of the p shell is completed. This surprising behavior is explained by a shift in the energy structure in favor of the coulomb repulsion due to the strong interaction in the hole system. We have mapped out the wave functions of electron and hole carriers using CV-spectroscopy with parallel magnetic fields. This allows us to obtain two dimensional plots of the probability densities in k-space for the carriers. The wave functions are interpreted in a quasi particle picture. For the s electrons in quantum dots we obtain Gaussian like probability densities with certain deviations. The wave functions are elongated along [1-10] in direct space. This is caused by a morphological anisotropy of the quantum dots and due to the piezoelectric effect in these structures. The p states show nodal structures with orbitals that are oriented perpendicular to each other. The low energy p states are oriented along [1-10] in direct space. The hole wave functions show an elongation along the perpendicular direction  in direct space. This confirms the assumption that the probability distribution is mainly influenced by piezoelectric effects in the strained semiconductor system. Using polarization dependent photoluminescence spectroscopy we demonstrate an energy shift in the interband transitions which indicates an anisotropic confining potential.