Simple wavefunction for an impurity in a parabolic quantum dot

A simple variational wavefunction is proposed for calculating the ground-state energy of a hydrogenic donor located at the centre of a spherical parabolic quantum dot. Binding energies are calculated for three values of the parameter which gives the strength of the confining parabolic potential by the proposed wavefunction as well as by a wavefunction used by Xiao et al. [Superlattices and Microstructures, 19, 137 (1996)]. The results are compared to the 'exact' energies obtained by numerical integration of the Schrodinger equation. It is shown that the proposed wavefunction gives considerably better results than the wavefunction used by Xiao et al. in all cases. (C) 1998 Academic Press Limited.