With the development of technological and experimental techniques

crystals with all kinds of dimension and shape have been made by experiment

which has brought out a large market for the apply of new materials. So there is continuing interests in polaron. Lee Low Pines calculated the ground state energy of polaron by a variational technique. Huybrechts calculated the energy of the ground state and the first internal excited state of the optical polaron for different values of the electron phonon coupling. N.Tokuda studied the dependence of ground state energy

effective mass and the mean number of polaron on the coupling constant by using the unitary transformation and the method of a lagrange multiplier. Larsen got the ground state energy of the two dimension magnetoplaron by using forth order perturbation theoretic method. Wei et al. investigated the cyclotron resonance mass and frequency of the interface polaron by using Feyman path integration method. Recently

Catandella et al. studied the properties of polaron in one dimension Holstein molecular crystals by using a new variational method

which chosen the linear overlap of Bloch wave of large polaron and small polaron as a trial wavefunction

obtained the variational regularities of the ground state energy

mass and the mean number of polaron with coupling constant. We also did some works on polaron by using Huybrechts' method. But all works were based on only one considering either magnetic field or coupling strength

respectively. This paper is going to illustrate the common influence of magnetic field and coupling strength on the properties of polaron. The variational relations of the ground state energy

self trapping energy and Landau energy with coupling constant and cyclotron resonance frequency are derived by using linear combination operator method. Numerical calculation indicates that the vibration frequency λ firstly falls

arriving to a minimum value

late increases with increasing coupling constant α;λ monotonously rises with increasing cyclotron resonance frequency ω c;the ground state energy

E

0

decrease with increasing α and monotonous rises with increasing ω c;the self trapping energy

E

0tr

increases with increasing α and ω c;Landau energy

E

0L

firstly increases to a maximum and then fall with increasing α;

E

0L

firstly rises to maximum also and then decreases with increasing ω c.