Compton effect: Schrödinger's treatment

**regel** · March 6th, 2010, 02:24 PM

Compton effect – the change of frequency and wave vector of X-ray radiation in process of scattering on free electron is usually considered as convincing demonstration of corpuscular aspect of electromagnetic field.

However Schrödinger has shown, that this effect can be completely explained by wave theory, without any necessity to enter the idea of corpuscular photon.

This explanation is based on Schrödinger's conception of real electronic field which is described by equation of his name.

Under the influence of X-ray radiation the resting electronic wave gradually comes to movement, and the motionless part of the electronic field together with moving part forms the standing wave. On this periodic structure X-ray radiation scatters just as light on the standing wave of ultrasound.

At the beginning of his paper Schrödinger (1927) wrote: “According to the wave theory of light all changes in frequency and wave normal can he predicted, as is well known, on the basis of very simple and general considerations on the phase, without going into any detail of the phenomenon... If the as*sumption is correct that with the de Broglie waves we have at hand a tool, equivalent to wave optics, for the treatment of those phenomena that were formerly understood exclusively as motions of particles, we should expect and demand that on the basis of simple phase considerations of the stated kind one should understand the changes in direction and frequency of the aether wave in the Compton effect connected with the velocity change of the electron”.

Detailed calculations on the basis of Schrödinger's was made by J. Strnad in 1986. The electronic field is described by quantum mechanics taking into account relativistic effects, and radiation – by classic electrodynamics.

The account of Bragg conditions and Doppler's frequency shift leads to the equations which in accuracy describe the experimental results received by observation of Compton effect.

Über den Comptoneffekt; von E. Schrödinger. Annale der Physik. 1927, 28, 257-64.
http://www.apocalyptism.ru/Compton-Schrodinger.htm

The Compton effect - Schrödinger's treatment. J. Strnad. Eur. J. Phys. 7 (1986), 217-221.
http://www.apocalyptism.ru/Comptoneffect-treatment.htm

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**J.C. Lavau** · May 13th, 2011, 11:51 AM

Thank you Lev Regelson for having re-published the papers from Schrödinger and Strnad. It has helped.

However both have failed in applying the Bragg law to the Compton diffusion, as in Broglie's waves the equidistance is twice what is required for a Bragg reflexion.

The right equidistance is only provided by the Zitterbewegung of the electron, whose spatial and temporal frequencies are double of the broglian ones.

The Bragg condition, drawed with only the reticular planes, without atoms at the nodes :

In the Compton diffusion, the only difference is that instead of cristalline planes, the interfering planes are the temporary standing electromagnetic waves, resulting of the sum of the ascending electronic Dirac-Schrödinger waves, and the descending ones.

The calculations are at
http://deonto-ethics.org/mediawiki/i...Zitterbewegung
Sorry, the text is in french.

So the right theoritical frame for the Compton diffusion, is relativistic, as for the Dirac equation in 1928, and for the initial Louis Victor de Broglie's hypothese in 1924 :
Every thing that has a mass m, has also an intrinsic and perpetual frequency, mc²/h.

So Broglie was led to the theorem of harmony of the phases, and to conclude that the phase velocity V is c²/v.

In 1930, Schrödinger has shown that the Dirac relativistic equation implies that a free electron has an electromagnetic oscillation, whose frequency is double the broglian frequency. Its usual name is "Zitterbewegung".

Here is an image of this Compton-Bragg-Schrödinger reflexion :

**J.C. Lavau** · May 22nd, 2011, 05:57 AM

The above result, that the Compton diffusion is explained by the Bragg reflexion, is met by storms of insults, by conformists.

Why ?

It ruins the hegemonic corpuscularist propaganda, all the "wave-corpuscle duality, cruel uncertainty principle, punctual nature of the electron, corpuscular nature of the photon, so on..."

The Bragg reflexion requires that the photon extends on several interatomic distances, even several tens of interatomic distances witdth and depth. It requires too that the reflecting crystallite has several tens of interatomic distances in width.

With the same mineralogical composition, a mineralogist or a geologist can easily distinguish a clay from a silt, just by knowing their X-Ray diffractograms. The silt has grains big enough to produce fine and high diffraction peeks. The clay diffraction peaks are much broader, much more fuzzy : the crystallites are not big enough for a precise angular reflexion.

In the Compton diffusion, the Dirac-Schrödinger standing waves of the reflected electron, are large enough for Arthur Compton establishing the law angle-frequency shift. Here "reflected" is meant in the center of inertia, though in the laboratory frame, the electron is seen as "ejected".

So the ejected electron has never become "small", and the photon never, too. Both remained several tens of interatomic distances deep and wide.

There is no corpuscles, only waves, with absorbers. But we have to consider an inferior horizon of validity of our familiar and macroscopic "space-time".

With or without John G. Cramer, the TIQM is unavoidable. We were several people to re-find it, independantly.

**J.C. Lavau** · June 15th, 2011, 06:59 AM