On the physical nature of the de Broglie wave
. Progress in Physics, 2016, v.
Experimental confirmation of the hypothesis of de Broglie wave
properties of electrons was carried out outstanding Britain experimental physicist George Thomson (1892-1975)--the son of the previously mentioned master of the world of physics Joseph John Thomson, who, irrespective of American experimental physicists Clinton Davisson (1881-1958) and Lester Germer (1896-1971) in 1927 discovered the diffraction of low-energy electrons (<<cathode rays>>) on a single crystal of nickel Ni [3, 4].
Mark Kasevich, Stanford University, Atomic de Broglie Wave
Navigation Sensors and Applications of Ultra-fast Electron Sources
i.e., the phase velocity of the inherent de Broglie wave
The Ray/3-Wave diagram that represents the Synge de Broglie wave
propagation in spacetime [2, p.
As discussed in , the Heisenberg Uncertainty Principle arises because x and p form a Fourier transform pair of variables at the quantum level due to the momentum p of a quantum particle being proportional to the de Broglie wave
number k of the particle.
It is well known, in quantum mechanics, a matter wave is determined by electromagnetic wave-particle duality or de Broglie wave
of matter .
and operate with the result on the wave function [psi](x, t) that represents the de Broglie wave
. We then obtain
This phase wave in terms of transmitting the particle mass at the speed v and angular frequency [[OMEGA].sub.d] = 2[pi]v/[[LAMBDA].sub.d], with [[LAMBDA].sub.d] and [[OMEGA].sub.d] obeying the de Broglie relations, represents a de Broglie wave
. The standing-wave function of the de Broglie (phase) wave and its variables for particle dynamics in small geometries are equivalent to the eigen-state solutions to Schrodinger equation of an identical system.
As a first approximation then, the electron and proton de Broglie waves
are planewaves propagating within the PV continuum.
Note 3: When incident on the crystalline foil, the electron beam must ensure a coherent and plane front of de Broglie waves
. Similar ensuring is required  for optical diffracting waves at a classical diffraction grating.