Calculation of the electronic energy eigenvalues and eigenstates and Coulomb and dipole matrix elements for realistically modelled quantum dots

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Using the information on the structure and the composition of the actual quantum dots from the experimental projects I-2, II-1 the electronic properties, i.e. the one-particle eigenenergies and the eigenstates shall be determined starting either from an effective confinement potential characterizing the QD or from a more microscopic tight-binding description of the QD. From the eigenstates one can calculate all one-particle and two-particle matrix elements, in particular the dipole matrix elements, which are important for the selection rules and thus for a calculation of the optical properties, and the Coulomb matrix elements. This leads to an effective Hamiltonian in second quantization with parameters determined for the actual QD. For a small number of electrons per QD this Hamiltonian can be solved exactly, otherwise an appropriate many-body approximation has to be applied to determine the relevant electronic properties including many-body effects.