The effect of the electron-phonon interaction on an electron bound to an impurity in a parabolic quantum well(PQW) has been studied theoretically in the past

but similar studies calculating the pola-rization potential in a PQW have not been reported.In this paper

the polarization potential and the binding energy of the bound polaron in the PQW are investigated.The study has taken the effect of bulk longitudinal optical(LO) phonons and the interface longitudinal optical(IO) phonons into account.By using the method of modified Lee-Low-Pines(LLP) variational method

the polarization potential and the binding energy of the bound polaron in the GaAs/Al

x

Ga

1-x

As PQW are obtained.The contribution of the impurity-phonon interaction to the total electron energy can be eliminated by the first canonical transformation

and the effect of this displacement on the lattice polarization leads to the polarization potential which partially compensates the electron-impurity Coulomb interaction.By the second canonical transformation

the ground state energy of the bound polaron in the infinite parabolic quantum well is worked out

and then the binding energy of the bound polaron can be gained by further calculations.The research results indicate that

the polarization potential is much smaller in the wider wells

but it is larger in the narrow wells

therefore

the polarization potential should not be neglected in the very narrow wells.For a given well width

the polarization potential decreases rapidly with increasing |

z

| and gets a minimum

then it increases with increasing |

z

| near the interface of the well.The contribution of the polarization potential to the ground state energy of the bound polaron decreases rapidly with increasing the well width(

L

) at first

and then decreases slowly with increasing

L

and approaches zero at large

L

.The binding energy of the bound polaron decreases rapidly with increasing

L

at the beginning

then decreases very slowly with increasing

L

and finally closes to the value of three-dimensional GaAs.In summary

the polarization potential should not be eliminated in a narrow PQW.