Phase Velocity And Group Velocity For Beginners

In the first section of this paper I derive the formulas for the phase velocity and group velocity as a function of the total relativistic energy and the momentum of a particle. In the second section I derive similar formulas as a function of the de Broglie and the Compton wavelengths of the particle. In the third section, I derive similar formulas as a function of the angular frequency and the wave number. Finally, two additional meanings of the Compton wavelength are derived. The first one is derived from the equation of the group velocity in terms of the de Broglie and the Compton wavelengths and the second one from the range of the weak nuclear force.