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Using a variational technique, the change of ground-state energy and binding energy of an impurity atom with impurity position and well width in a GaAs-${\mathrm{Ga}}_{0.7}$${\mathrm{Al}}_{0.3}$As quantum well is calculated. In the calculation the electron--surface-optical-phonon interactions are taken into account. The result is discussed. It is found that the electron-phonon interaction energy depends not only on the width of the well but also on the position of the impurity atom in the well.