Since Ibach

c

arried out low-energy electron diffraction experiments on ZnO semiconductor surface

the properties of the surface polaron in crystals have been of considerable interest.Many investigators studied the properties of the surface magnetopolaron by the method of a perturbation

a Larsen’s

a linear combination operator

a variational

a Feynman’s path integral

and a Green function et al.The present author and co workers discussed the ground state energy

vibration frequency and effective mass of the surface magnetopolaron by the method of a linear combination operator and a Lagrange multiplier.Many of them mainly concentrated their attention on the ground state energy case.However

fewer works have been done on the research of the properties of excited state of surface magnetopolaron.In the early 1970s

the energy of the ground and the first internal excited state of the optical polaron calculated by Huybrechts.The first relaxed excited state energy of the free Frohlich polaron was evaluated using the Fock approximation of Matz and Burkey by Lepine.Chunetal.discussed the hydrogenic impurity binding energy of the ground and the excited state in a cylindrical quautum wire by using Landau and Pekar variational method.The effect of confined electron optical phonon interaction on the binding energies of the ground state and an excited state are calculated as a function of wire radius.Using a similar method to that of Gu et al.and minimizing the energies to determine the variation parameters Luetal.

calculated selfconsistently the ground state and the first excited state energy shifts of a polaron in a slab due to the interactions of the electron with the BO and SO phonons.The gound state

excited states energy and selfenergy change with temperature were investigated using Green function method by Qin et al..Following the perturbation theory of Bajaj et al.

the ground state energy of a bound piezopolaron is computed for ZnS

ZnTe and CdTe by Sivakumar et al..Extending this theory to the excited states

the LA phonon contributions to the Lamb Shifts in these piezoelectric semiconductors are obtained.The energy of the internal excited state

the excitation energy and the vibration frequency of the weak coupling surface magnetopolaron are calculated by using the linear combination operator and the unitary transformation methods.Two limiting cases are discussed.As an example

the numerical calculation for ZnSe crystal has been carried out.The results show that the excitation energy and vibration frequency of the surface megnetopolaron will increase with increasing the magnetic field.