Relating the probability distribution of a de Broglie wave to its phase velocity

Malcolm H. Mac Gregor

Pingxiao Wang, Jiaxiang Wang, YuKun Huo +2 more

We show that the phase velocity in a stationary state of a de Broglie wave can be directly obtained from the probability distribution, i.e. the quantum trajectories, without detailed knowledge of the phase term itself. In other words, the amplitude of a de Broglie wave function describes not only the probability distribution but also the phase velocity distribution. Using this relationship, we comment on two calculations of the Goos-Hänchen shift in de Broglie waves.

Patrick Marquet

Wu Tian

From the viewpoint that de Broglie wave is probability wave,this paper explored the velocity characteristics of the de Broglie wave and built the relation between phase velocity and group velocity.

Igor Pavlovich Popov

It is shown that the experiments on interference and diffraction of single particles allow to set indirectly the phase velocity of de Broglie waves. The author considers the possible start and end times of the interference pattern during the passage of a single particle through one of the slits of a device for observing the particle interference. It is found that if the phase velocity is less than the velocity of the particle, the particle will come to the detector before the interference occurs, so its location is not subject to the distribution of the probability density which will be available later. At the same time, if the phase velocity is greater than the velocity of the particle, the particle will come to the detector when the interference pattern is over, so the location of the particle will not obey the distribution of the probability density which no longer exists. As a result, it is found that the phase velocity of de Broglie waves is equal to the speed of the particle.

Malcolm H. Mac Gregor