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Journal of Weifang University

Phas s Velocity Group Velocity and de Broglie wave

Bo Jiang

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

After introduce phass velocity and group velocity.from de Broglie relation, discussed particles waVe-praticle duality.GiVe the Velocity of particle that is the groug Ve101 ity of de Brogl ie wave

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•Jan 1, 2015•1 citation
For the wave-particle duality of microscopic particles,the relationship of the velocity and the velocity of phase and the velocity of group for the microscopic particles is analyzed,it is pointed out that the velocity relating to the frequency and wavelength of two De Broglie expressions is not the velocity of group but the velocity of phase.On the contrary,the velocity in the defining expression of momentum is the real speed of particles,which doesn't equal to the velocity of phase but equals to the velocity of group.
The de Broglie relation is revisited in connection with an ab initio relativistic description of particles and waves, which is the same treatment that historically led to this famous relation. In the same context of the Minkowski four-vector formalism, we also discuss the phase and the group velocity of a matter wave, explicitly showing that both transform as ordinary velocities under a Lorentz transformation. We show that such a transformation rule is a necessary condition for the covariance of the de Broglie relation, and stress the pedagogical value of the Einstein-Minkowski-Lorentz relativistic context in the presentation of the de Broglie relation.
The identification of particle velocity with the velocity of a wave group was a crucial assumption that resolved important inconsistencies in the theoretical developments of Louis de Broglie and Erwin Schrödinger. Interestingly, this was one of the few common aspects of their work. In this paper, we present a reconstruction of how group velocity became essential for both de Broglie and Schrödinger, as well as a comparison of important differences in their theories. Pedagogical lessons to be extracted from this episode are also outlined.
This article points out a falsehood in some documents about the relations between the velosity of singlw phase and group phase of de Broglie wave,and explains that the superlight velosity of wave phase is not contracted with wave-particle duality.The article makes a further study of diffusion of de broglie wave packet and comes to a cvonclusion that the smoothly changing wave packet of free particle and frequency spectrum functionφ(k) is basically not diffusing,on the contrary,it diffuses faster and apparently.
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.