With the development of the growth techniques of the semiconductor

the well performanced heterostructures

quantum well and superlattice have been prepared

which is the great breach in Semiconductor physics and material science.The problem of confined electron in a quantum well(QW) has attracted much interest from physicists in recent years. Zhao

et al

. calculated the ground state

the first excited state and the transition energy of the electron(or hole) in the GaAs/Al

0.3

Ga

0.7

As parabolic quantum well by using a mo-(dified) Lee-Low-Pines variational method. Chen

et al

. investigated polaronic effects in a quantum well by using the Landau-Perkar theory. Comas

et al

. and Rücker

et al

. calculated self-energy of polaron and mageneto-(polaron) in a quantum well by use of the standard perturbation-theory. Chou

et al

. studied the ground state binding energy of hydrogenic impurity in a quantum well by using a general perturbative method proposed by Lee and Mei. Shen

et al

. discussed the binding energies of the hydrogenic donor ground state in a GaAs-Ga

1-x

-Al

x

As quantum well of finite barrier height in presence of a magnetic field

which is taken to be parallel to the growth axis of the quantum-well structure by using strong-perturbation theory and pertubative-variational approach. Ren

et al

. calculated the ground-state energy of a polaron in parabolic quantum well in the presence of a Coulomb potential by using Feynman-Haken path integral theory.Eerdunchaolu

et al

. studied the tempe-(rature) dependence of the properties of electron-bulk LO phonon interaction system in a quantum well within (the electric-magnetic) fields along the growth axis by using variational wave-function and harmonic oscillator (operator) algebra method.The properties of the polaron in a quantum well are seldom investigated by using a linear-combination-(operator) method. In this paper

the properties of ground state of the polaron in an finite quantum well were investigated. The vibration frequency

ground state energy and ground state binding energy of the strong-coupling polaron in an infinite quantum well

the effects of well width L and electron-LO phonon coupling strength α on the vibration frequency λ

ground state energy E

0

and ground state binding energy E

b

of the strong-coupling polaron were discussed by using a linear-combination-operator and variational method. Numerical calculation (illustrates) that the vibration frequency and ground state binding energy of strong-coupling polaron in an infinite quantum well will decrease with increasing well width L and increase with increasing the coupling strength α;the ground state energy will decrease with increasing L and its absolute value will increase with increasing coupling strength α; our results approach those of 2D and 3D polarons respectively in the limits of small and large well width L.