With the development of several experimental techniques

for example

molecular beam epitaxy

metal-organic chemical-vapour deposition and electron beam lithography combined with reverse mesa etching

there has been a lot of work devoted to the understanding of hydrogenic-impurity states in low-dimensional semiconductor heterostructures such as quantum wells

quantum wires and quantum dots. In recent years

there has been great interest in investigating quantum dots both theoretically and experimentally. Due to the small structures of QD’s

some physical properties such as optical and electron transport characteristic are quite different from those of the bulk materials. The study of the impurity states in these low dimensional structures is an important aspect to which many theoretical and experimental works based.In recent years

the physical characteristic of a bound polaron in a quantum dot has been of considerable interest. Wang

et al

. investigated influence of the LO phonon on the ground state energy of the hydrogen-like impurity in a spherical semiconductor quantum dot by using variational method. The expression of the ground-state energy of an electron coupled simultaneously with a Coulomb potential and a longitudinal-optical phonon field in parabolic quantum dot and wires within the frame-work of Feynman variational path-integral theory are derived by Chen

et al

. Melnikov

et al

. studied the effect of the electron-phonon interaction on an electron bound of an impurity in a spherical quantum dot embedded in a nonpolar matrix theoretically. The all-coupling variational method is used to calculate the polaron energy shift including interaction with both bulk and surface LO phonons.Bound polarons are discrete

confined electronic states

spatially localizd due to a local potential

V

(

r

)

but sharing a common phonon state of the surrounding crystal. Woggon and Miller studied the energy states of polarons bound in a potential and determine the local optical absorption spectrum using first-order time-dependent perturbation theory with respect to the electron-phonon interaction. However

few of investigators studied the bound polaron in the quantum dot with the improving linear combination operator method so far.In the present paper

by using the improving linear combination operator and unitary transformation method

properties of the bound polaron in a parabolic quantum dot are studied for the weak electron-LO-phonon coupling case. Results show that the interaction energy of the weak-coupling bound polaron will decreases with increasing the Coulomb potential

the effective confinement length of quantum dot and the electron-LO-phonon coupling strength increasing. The vibration frequency of the weak-coupling bound polaron will decrease with increasing the effective confinement length

but will increase with increasing the Coulomb potential and the electron-LO phonon coupling strength. Meanwhile

the interaction energy and the vibration frequency will increase sharply with decreasing the effective confinement length. Those attribute to interesting quantum size effects.