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 semiconductor heterostructures such as quantum wells

quantum wires and quantum dots.In recent years

there has been great interest in investigating the problem of a bound magnetopolaron in a parabolic quantum wires both theoretically and experimentally.And a lot of work has also been devoted to study the properties of the bound magnetopolaron in a parabolic quantum wires by kinds of methods.However

by using a linear combination operator and unitary transformation method to study it is seldom.The properties of the bound magnetopolaron in a parabolic quantum wires were studied by using a linear combination operator and unitary transformation method.The ground state energy

the vibration frequency and the mean number of optical phonons of both weak-coupling and strong-coupling bound magnetopolaron in a parabolic quantum wires calculated respectively.The influence of the electron-phonon coupling strength

the cyclotron frequency and the confinemend length of the quantum wires on the ground state energy

the vibration frequency and the mean number of optical phonons of the bound magnetopolaron in a parabolic quantum wires were discussed.More obviously the variational relation of the ground state energy

the vibration frequency and the mean number of optical phonons with the electron-phonon coupling strength

the cyclotron frequency and the confinemend length of the quantum wires were studied.Numerical calculations were performed for GaAs quantum wire

as an example

and the results illustrated that the ground state energy

the vibration frequency and the mean number of optical phonons in a parabolic quantum wires will increase with increasing the confinemend length of the quantum wires and the magnetic field

for both weak-coupling and strong-coupling bound(magnetopolaron)and they will increase with decreasing the Coulomb potential and the electron-phonon coupling strength.