Since Esaki and Tsu composed semiconductor superlattice

the special properties of electron in superlattice and heterostructure have been investigated by many persons.Especially for cylindrical quantum wire

a lot of works have been done.The Hamiltonian for the electron-LO phonons interaction in cylindrical QW has been derived by Constantinou and Ridley following the calculation of continuum model.Using variational method

Zhou studied the size dependence of the ground state energy

excited energy and cyclotron resonance frequency of magnetopolaron in cylindrical QW.Considering the interaction of electron-SO phonons

Buonocore investigated the self-energy of polaron by using the transformation and the variational methods and also studied the ground state and the first excited state self-energy of magnetopolaron.Employing LLP mediate coupling method

Sheng investigated the self-energy and effective mass of polaron in which the interactions of electron-LO phonons have been taken into account.Hua studied the self-energy and effective mass of polaron by using LLP transformation and also using the variational methods

he investigated the relation between the ground state energy

the electron-SO phonons interact energy of excited state and cyclotron resonance frequency of magnetopolaron.Employing LLP variational approach and perturbation method

Xie studied the polaron effect in a freestanding quantum wire.Considering the interaction of electron-LO phonon

Ding studied the systematic ground state energy and the interact energy of electron-LO phonon.In this paper

the size dependence of the mean number of optical phonons of polaron in cylindrical quantum wire was investigated by using the LLP variational approach and taking into consideration of the electron-bulk LO phonon coupling.Numerical calculations are performed.The result illustrates that the mean number of bulk LO phonons of polaron N will decrease with the decreasing

R

(the radiu of cylindrical quantum wire's cross section) and it will increase with increasing coupling strength.The coupling strength will increase with decreasing

R

.