Abstract: By using Laurent series, the velocity (～c) is expanded and then the total energy expression of a particle moving with high velocity is obtained. The total energy contains two parts: the reste nergy and the kinetic energy. Also in this paper the theory of the de Broglie wave from the relation of the energy-momentum is obtained in which the phase velocity is still less than the velocity of light c.

Key words: super nonlinear total energy, kinetic energy, rest energy, momentum, de Broglie wave