In this paper, we derive the quantum Vlasov equation as a differential equation of the Wigner function directly from the electromagnetic Schrodinger equation and apply it to the plasma waves propagating in the direction parallel to the ambient magnetic field. The upper branches of the L and R waves in the plot of (omega, k) space have dispersion relations similar to those of their respective classical waves, with only minor corrections. The lower R-wave branch also has a dispersion relation similar to that of the classical whistler wave for a small wavenumber k. However, the dispersion curve encounters a region of anomalous dispersion, exhibiting a negative group velocity, as k increases. Furthermore, the branch becomes a damping wave as k increases above a certain critical value and eventually the wave becomes ill-defined for larger k values. Published under license by AIP Publishing.