With recent rapid development of epitaxial techniques such as molecular beam epitaxy(MBE) and metal organic chemical vapor deposition(MOCVD)

there has been great interest in investigating quantum well and wires both in materical science and condensed state physics field.Due to the electron motion along the length of the wire is free size and is quantized in the two dimentions perpendicular to the wire in quantum wires

they had a series of new and serious special physical properties which are quite different from those of the semiconductor constituents.These had brought infinite chance and hope on development and use of new materials.Especially

electron in quantum wire was subject to a two-dimension confinement

so that quantum effect was quite different from those of the bulk metericals

these would brought about great society benefit and economic benefit.So many scientists have been investigating properties of quantum wires.Francisco has stu-died the hydrogenic impurity binding energy in QWWS;Chuu et al.have calculated the energies of the ground state and the excited state in cylindrical quantum wires using Pekar alternative approach and peturbration-variational approach.Zhou and Gu have discussed the properties of polaron and magetopolaron in cylindrical quantum wires and in rectangular quantum wires by using variational solutions and linear combination operators me-(thods.) Guo et al.have investigated the electron-optic effects of double-layered quantum wires in magnetic field by means of density-matrix treatment.In this paper

taking into account the interaction of the electron with optical phonon modes in parabolic quantum wires

we have investigated weak-coupling polaron effective mass and the mean number of optical phonon by using of Tokuda's improved linear combination operators

the Lagrange multiplier and the variational method.Numerical calculations

for the ZnScrystal as an example

are performed.The results indicated that

both the effective mass m

*

of polaron and the mean number of optical phonon Nincreased with the increasing of Lagrange multiplier u.With the increasing of confinement strength ω

0

of quantum wire

vibration frequency λ of polaron would increase.In short

both the effective mass m

*

and the mean number of optical phonon Nof polaron increase with the increasing of Lagrange multiplier u as well as(vibration) frequency λ of polaron increase with increasing of confinement strength ω

0

for weak-coupling in a parabolic quantum wire.