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

利用实验项目I-2、II-1中实际量子点的结构和组成信息，可以从表征量子点的有效约束势或更微观的量子点紧密结合描述出发，确定电子特性，即单粒子本征能和本征态。从本征态可以计算出所有的单粒子和双粒子矩阵元素，特别是偶极子矩阵元素，这对选择规则和光学性质的计算都很重要，以及库仑矩阵元素。这导致了二次量化中有效的哈密顿量，其参数为实际量子点确定。对于每个量子点的电子数量很少，这个哈密顿量可以精确求解，否则必须应用适当的多体近似来确定包括多体效应在内的相关电子性质。

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.