Dispersion relations for parallel propagating waves in magnetized quantum plasma

We derived the quantum Vlasov equation in a differential form based on the Wigner distribution function and applied the equation to parallel propagating waves in magnetized quantum electron plasma. Whereas the resulting electrostatic dispersion relation for a Langmuir wave is the same as the one obtained previously from the fluid approach, the behaviours of the electromagnetic dispersion relations are different from those of the fluid ones, which have been obtained to be the same as the classical dispersion relations. It is found that the degeneracy effect is to increase both the phase and the group velocities of the upper branches of the L and R waves whereas it decreases those of the whistler wave. It is also seen that the quantum effect on the R wave is larger than that on the L wave. In the long wavelength limit, the degeneracy effect is shown to be dominant over the quantum kinetic effect.