Considering the image potential, we calculate the binding energies of
a shallow donor impurity placed on the centre of a quantum box using t
he variational approach. The results we have obtained show that there
is a great difference of the effects of image potential between the ca
ses including impurity ion image potential and including the image pot
entials of impurity ion and electron simultaneously. The results also
show that the image potential is important, especially when the dimens
ions of quantum box become small.