In the early 1980’s

Tokuda studied the mean number of phonons for both the optical and the piezoelectric polarons within the scheme of variational approach based on the unitary transformation and the method of the Lagrange multiplier.Many investigators studied the properties of the mean number of phonons of polarons by using many methods. The properties of the mean number of phonons of the polaron in polar crystal

quantum well

quantum wire and symmetric quantum dot have been studied using the linear combination operator method by one of the present authors and co-worker. Recently

the mean number of phonon of the polaron in an asymmetric quantum dot has been calculated using linear combination operator method by the present author. However

using linear combination operator method

the properties of the mean number of phonons for the bound polaron in an asymmetric quantum dot has not been investigated so far. The purpose of this present paper is to explore the effect of the transverse and the longitudinal effective confinement length of quantum dot

the Coulomb bound potential and the electron-phonon coupling strength on the properties of strong-coupling bound polaron in an asymmetric quantum dot. We obtain the expressions for the vibration frequency and the mean number of phonons of the strong-coupling bound polaron in an asymmetric quantum dot as a function of the transverse and the longitudinal effective confinement length of quantum dot

the Coulomb bound potential and the electron-phonon coupling strength by using linear combination operator and the unitary transformation methods. Numerical calculations are performed and the results show that the vibration frequency and the mean number of phonons of the strong-coupling bound polaron in an asymmetries quantum dot will strongly increase with decreasing the transverse and longitudinal effective confinement length of quantum dot

and will increase with increasing the coulomb bound potential and the electron-phonon coupling strength.