Using a simple model of a two-dimensional rectangular quantum box we study the effects of size and anisotropy on the energy and photoluminescence spectra of neutral and charged quantum dots. The competition of symmetries and energy/length scales of the free exciton or trion and of the confining potential is analyzed. The numerical calculations consisted of the diagonalization of the few-electron-hole Hamiltonian matrices in the full configuration-interaction basis, with the simultaneous resolution of the conserved orbital and spin quantum numbers.
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