A study of variational wave functions for calculation of the ground-state energies of excitons confined in a two-dimensional (2D) disc-like and three-dimensional (3D) spherical parabolic GaAs quantum dots (QDs) is presented. We have used four variational trial wave functions constructed as the harmonic-oscillator basis multiplied by different correlation functions. The proposed correlation function formed by including linear expansion in terms of Hylleraas-like coordinates to the Jastrow factor is able to capture nearly exactly the ground-state energies of 3D excitons, and it properly account for the results of 2D excitons. Quantum Monte Carlo techniques combined with the proposed wave function are a powerful tool for studying excitons in parabolic QDs.
Interaction effects in the mesoscopic regime: A quantum Monte Carlo study of irregular quantum dots
