The de Broglie wave packet for a simple stationary state

L. Mackinnon

L. Mackinnon

Gary P. Dillon

Layton A. Hall, Ayman F. Abouraddy

W. E. Baylis

De Broglie waves are a simple consequence of special relativity applied to the complex-phase oscillations of stationary states. As de Broglie showed in his doctoral thesis, the synchronized oscillations of an extended system at rest, even a classical one, become de Broglie-like waves when boosted to finite velocity. The waves illustrate the well-known but seldom demonstrated relativistic effect of clock desynchroniation (or dephasing) in moving frames. Although common manifestations of stationary-state oscillations in interference experiments are sensitive only to energy differences, de Broglie wavelengths are inversely proportional to rest-frame oscillation frequency, and their observed values require that the oscillation frequencies are proportional to the the total absolute energy, including the rest component mc2. PACS Nos.: 03.65.Ta, 03.30.+p, 01.65.+g

Malik Mohammad Asif

The original wave theory proposed by de Broglie necessitates a stationary (localized) monochromatic plane wave of high frequency νo associated with particle. As particle moves the de Broglie wavelength appears as an observable (a relativistic effect). The nature and interpretation of high frequency oscillations remained unrevealed so far. This paper presents a self trapped circular Electromagnetic (EM) travelling wave model of Electron (specifically) and other charged particles generally. Curling EM wave is localized (stationary) and still a plane monochromatic travelling wave, against the customary wave packet approach, where number of frequencies are made to interfere to build a stationary localized wave-packet. The model reveals facts such as interpretation of wave function ψ (de Broglie wave) as a relativistic effect of a real wave function and removes the discrepancy of very high phase velocity (c 2 /v) associated with it. The model also incorporates zitterbewegung of electron and 4π rotation needed, for a complete round of wave cycle.