The properties of the electron-ripplon system on the surface of liquid helium film in a magnetic field influence the properties of liquid helium very markedly. The problem of a 2D electron on the surface of a liquid helium film was formlated by Jackson and Platzaman as a surface polaron problem. The properties of electron-ripplon system on the surface of liquid helium film in a magnetic field have been of considerable interest. In recent years the ripplon problem in a magnetic field has been studied by many theoretical methods and the properties of the ripplonic polaron in a magnetic field are measured using experimental method by many investigators. An electron on the surface of a liquid-helium film in a uniform magnetic field is studied as a polaron problem by Kato and Tokuda by an extended variational scheme of the Lee-Low-Pines theory.Using the harmo nicos cillator algebra

Lin

Chen and Jin calculate the ground-state energy of the system of an electron coupled to a ripplon on the outer surface of the liquid-helium film under the influence of a magnetic field of arbitrary strength. By means of a variational scheme of the Pekar type

a system of strongly coupled ripplonic polarons on the outer surface of liquid-helium film under the influence of a mag netic field of arbitrary strength is studied by Chen and Jin.Cesar et al. determined the energy spectrum of the surface electrons on liquid helium films in the presence of a perpendicular applied magnetic field by different approaches within second order perturbation theory.We studied the properties of the surface magnetopolaron in polar crystals by using a linear com bination operator method. However

by means of a linear combination operator method

the research on the pr operties of the electron-ripplon system on the surface of liquid helium fimls in a magnetic field has not been studied so far. The properties of the surface electron weakly and strongly coupled with ripplon on films of liquid helium in amagnetic field are studied. The vibrational frequency and ground state energy of the surface electron-ripplon system on liquid-helium films in amagnetic field was derived by using a linear combination operator method. The results show that

for the strong coupling the vibrational frequency λ of the surface electron-ripplon system on liquid hel ium films in a magnetic field will increase with increasing electron-ripplon coupling constant α and magnetic field

B

whereas the ground state energy

E

0

will increase with increasing electron-ripplon coupling constant α and with de creasing magnetic field

B

.