Abstract
The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. According to the special relativity theory, the group velocity with which the overall envelope shape of the wave, namely the related particle’s propagation and information convey speed is changeable with its energy and related wavelength, among which only the energy exceeds over the minimum value, the propagation can be starting and the velocity is not allowed to surpass the maximum value i.e. the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 8.187×10ˉᴵ⁴J and the related wavelength is shorter than around 5.316×10ˉ³nm, the matter wave with information can start to propagate.
Highlights
The Wave-Particle Duality is a basic property of microscopic particles
As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments
According to the special relativity theory, the group velocity with which the overall envelope shape of the wave, namely the related particle’s propagation and information convey speed is changeable with its energy and related wavelength, among which only the energy exceeds over the minimum value, the propagation can be starting and the velocity is not allowed to surpass the maximum value i.e. the light speed in vacuum
Summary
Wave-Particle Duality is a basic property of microscopic particles [1]. Inspired by Albert Einstein’s light wave-particle duality theory [2]. De Broglie concluded that the velocity of a particle should always be equal to the group velocity of the corresponding wave This conclusion had been proved for free particle’s non-relativistic propagation [11] and can be proved for free particle’s relativistic propagation as below: According to the special relativity theory, particle’s total energy E is. De Broglie considered that not all matter move with the velocity of light speed in vacuum, so he changed the mass- energy equation from E=mc to E=mv by replacing c with the actual velocity v and equal both as mv2= hν This important change means that the de Broglie hypothec did not take the relativity theory as its theoretical base and the propagation is non-relativistic [11]
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