With the development of several experimental techniques

for instance

metalorganic chemical vapour deposition

molecular beam epitaxy and electron beam lithography combined with reverse mesa etching

there has been of considerable interest in understanding of hydrogenic-impurity states in low-dimensional semi conductor heterostructures such as quantum wells

quantum well 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. Recent investigations in the reduced dimensionality show that the impurity binding energy will be enhanced with the deduction of the dimensionality. In recent years

the problem of a bound magnetopolaron in a quantum dot has been extensively studied. Petukhov etal. studied the hopping and giant magnetoresistance of a bound magnetic polaron in magnetic semiconductors and nanostrucrure with the golden rule at effective mass approximation. Charrour etal. presented a systematic study of the ground state binding energy of a hydrogenic impurity in cylindrical quantum dot subjected to an external strong magnetic field and performed calculations within the effectivemass approximation using the variational procedure and considering an infinite confining potential on all surfaces of the system. Liu et al. investigated properties of the bound magnetopolaron in a quantum wires. Bouhassoune et al. studied magnetic field effect on the binding energy of a bound polaron in a quantum well by a variational method. Nguyen et al. analysed magnetic field effects of parabolic confining potentials on the binding energy of hydrogen impurities in quantum dots using a very simple trial function with only one variational parameter. Chen etal.derived ground state properties of the bound magnetopolaron using the linear combination operator and unitary transformation method. Corella etal. calculated the ground state and binding energy for the hydrogen impurity in a spherical quantum dot by using the variational method. Zhou etal. derived energy levels of the bound magnetopolaron by the variational method. Li et al. investigated the influence of magnetic field on the binding energy of a hydrogenic impurity in cubic quantum dots

and so on. In the present paper

by using the linear combination operator and unitary transformation method

properties of the bound magnetopolaron in a parabolic quantum dot are studied for the strong electronLOphonon coupling case. Results show that the vibration frequency of the bound magnetopolaron decreases with the cyclotro resonance frequency

the effective confinement length increasing and it increases with the Coulomb potential increasing. The average number of phonons decreases when the effective confinement length

the cyclotron resonance frequency increased

and it increases when the Coulomb potential enhanced.