In this paper, by using a quantum hydrodynamic plasma model which incorporates the important quantum statistical pressure and electron diffraction force, we present the corrected plasmon dispersion relation for graphene which includes a k quantum term arising from the vector). The longitudinal plasmons are the electrostatic collective excitations of the solid electron gas. We have tried to use the quantum hydrodynamic model for studying of propagation of the electrostatic surface wave in single layer graphene, in the presence of an external and uniform magnetic field. The direction of magnetic field was selected in plane of graphene sheet. It shows the importance of quantum term from the collective electron density wave interference effects. By plotting the dispersion relation derived, it has been found that dispersion relation of surface modes depends significantly on these quantum effects (Bohm’s potential and statistical terms) and it should be taken into account in the case of magnetized or unmagnetized plasma; we have noticed successful description of the quantum hydrodynamic model. The quantum corrected hydrodynamic model can effectively describe the Plasmon dispersion spectrum in degenerate plasmas, since it takes into account the full picture of collective electron-wave interference via the quantum Bohm’s potential. By plotting the normalized dispersion relation, the behavior of two different wave types (lower- and higher- branches) was predicted. It was found that the lower-branch should not be propagated to the specific wave number (cut-off frequency). By drawing of the contour curve of the lower- and higher-branches modes, the areas that modes can be propagated were obtained. So, Quantum hydrodynamic model is an effective way to study the waves in various media.
