  The linewidths and the energy shifts of the resonant states of the impurity
electron in GaAs-based quantum wells (QWs) with infinite barriers are
calculated. The two-dimensional Schr\"{o}dinger equation for the charge
impurity in the QW is solved by the developed finite-difference method combined
with the complex-scaling technique. A dependence of the linewidths and energy
shifts on the QW width for the impurity localized in the center of QW is
studied. The calculated results extend and improve theoretical estimations of
these quantities in the GaAs-based QW by Monozon and Schmelcher [Phys. Rev. B
71, 085302 (2005)]. In particular, in agreement with their studies we obtain
that resonant states originating from the second quantum-confinement subband
have negligibly small linewidths. In contrast to previous estimations, we show
that for the QW widths of the order of the impurity's Bohr radius the
linewidths of resonant states associated to the third quantum-confinement
subband linearly depend on the thickness of the QW. We show how the previous
theoretical predictions can be improved for such QW widths. We also calculate
linewidths for the case when the electron impurity is localized away from the
center of the QW.
