A time-dependent approach for the calculation of eigenenergies, eigenfunctionsand optical spectra, within the effective-mass and single-hole-bandapproximations, of low-dimensional semiconductor systems is presented. In thismethod, energy and optical spectra are obtained by Fourier analysis of atime-autocorrelation function constructed from an appropriately chosenpropagated wavepacket. Eigenfunctions are determined by a direct Fourieranalysis of such a propagated wavepacket. The time evolution of the wavefunctionis obtained by numerical integration of the time-dependent Schrödingerequation. This approach shares the virtues of the more common numericalmethods (accuracy, flexibility and automatic enforcement of boundaryconditions) with the additional advantage that it can yield an entire eigen oroptical spectrum in a single calculation. The methodology is applied to thecalculation of all the eigenenergies and eigenfunctions of the conductionband, and the intensities of the transitions from the ground state of thevalence band to all the states of the conduction band, in sphericalGaAs-(Ga,Al)As quantum dots with finite confinement and a wide range of radii,without and with an on-centre shallow donor impurity.
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