With the development of several experimental techniques

for example

metalorgnic 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 semiconductor heterostructures such as quantum wells

quantum wires

and quantum dots.In recent years

there is of great interest in investigating quantum dots both theoretically and experimentally.Due to the small structures of QDs

some physical properties such as optical and electron transport characteristic are quite different from those of the bulk materials.The study on the impurity states in these low dimensional structures is an important aspect on which many theoretical and experimental works based.Recently there has been a considerable number of theoretical studies on the effect of a bound magnetopo-laron in a parabolic quantum dot.However

there has very few article on the properties of the internal excited state of bound magnetopolaron by using the linear combination operator in parabolic quantum dot up to date.In this paper

by using the linear combination operator and the unitary transformation method

the properties of the excited state of the weak-coupling bound magnetopolaron in a parabolic quantum dot were calculated.The relation of the vibrational frequency

the first internal excited state energy

the excitation energy and the resonance frequency of the weak-coupling bound magnetopolaron with the effective confinement length of the quantum dot

the Coulomb bound potential

the electron-LO-phonon coupling strength and the cyclotron frequency in a parabolic quantum dot were obtained.Results show that he vibrational frequency

the first internal excited state energy

the excitation energy and the resonance frequency of the bound magnetopolaron increase rapidly with decreasing the effective confinement length in the electron-phonon weak-coupling case in a parabolic quantum dot.They also increase with increasing the Coulomb bound potential and decreasing the electron-phonon coupling strength.