We have presented a numerical calculation of the excitonic absorption
spectra in finite parabolic Ga1-x Alx As quantum well of different widths and
heights. First, we evaluated the exact analytic single particle ground State
solutions, in terms of Kummer functions as detailed by Wu-Pen Yuen
[Phys.Rev.B 48, 17316 (1993)], for an electron and a hole. The binding energy
of an exciton bound to the quantum well structure is then determined using a
standard variational technique. To investigate the excitonic optical absorption
near the energy gap, we used a generalized Elliot's formula originally proposed
by P.Lefebvre, et.al. [Phys. Rev. B 48, 17308 (1993)]. The model is based on a
simple concept that the exciton confined to a quantum well can be
approximately characterized by a single parameter, namely the fractional
dimensional parameter α . Within this model, we include not only bound states
contribution, but also the effects of the unbound states, which enhances the
continuum absorption above the energy gap.