Today I found an interesting paper by G. Poelz (retired from Hamburg University) which suggests that electrons have wave character, see http://arxiv.org/pdf/1206.0620.pdf. Basically he describes an electron model based on the solution of the wave equation in spherical coordinates (see Appendix 6.2 in his paper). This would need the use of spherical Bessel functions of the first kind (see for instance: http://mathworld.wolfram.com/SphericalBesselFunctionoftheFirstKind.html).
Interestingly, I found that George Shpenkov also uses a similar method to describe not only electrons but other atoms as well, based on the solution of the wave equation in spherical coordinates. See his page at this www.researchgate.net or at http://shpenkov.janmax.com. Shpenkov asserts that his method is different from the electron cloud model based on the Schrodinger equation.
While of course this kind of electron model may be different from the standard picture, it seems to be able to fulfill Louis de Broglie's vision in his Nobel lecture: Wave nature of electrons. (see http://www.nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf)
So do you think it is possible to find an exact electron model based on the solution of the wave equation in spherical coordinates?
As far as I understood the paper by Poelz, he is interested in a classical picture of the electron that opens up a closer "approximation" to quantum mechanics. Essentially, the classical picture of the electron in his approach is a massless charged particle that is bound in the radiation it emits and thus, aquires a mass and a smearing of the charge into a distribution of small radius. This is similar in spirit to the Zitterbewegung in quantum mechanics where a massless particle is considered to interact repeatedly with a field - eg. the Higgs field - in a nonlinear way, also aquiring a mass by the interaction.
I doubt that the nonlinear classical equations of Poelz will yield to an exact solution, in view of the complicated shapes occurring in his figures derived from numerical calculations.
Dear Herbert, thank you for your answer. Yes perhaps Poelz's electron model seems too complicated. But it could be one step toward a model of electron based on wave equation. You can compare with Shpenkov's model which is also derived from classical wave equation. Furthermore, is there a model of electron in quantum mechanics? As far as i know, in quantum mechanics, the wave mechanics asserts that we can only know the probability of existence of electron in a location (electron cloud), but it is forbidden to say anything about the nature of electron itself. Best wishes
As regards Shpenkov, he seems to try to invent a physics and a mathematics on his own. I recommend to be extremely cautious in taking over his theoretical approaches. He even argues against using imaginary numbers in the sciences....
Dear Herbert, ok thank you for your suggestion. Btw, another question: do you think that electron model can be related to a new concept like self-organized criticality? I have heard about SOC sometime ago, but do not find any equation yet. Thanks
Dear Aly, thank you, but i am not sure what do you mean with yes? please explain. thanks
Hello Victor,
If an electron is a charged photon, then the wave physics of photons should also apply to the electron, except that the normal photon is a boson while a charged photon would be a fermion. See https://www.researchgate.net/publication/266392325_The_Electron_Is_a_Charged_Photon
I saw you discussed my arxiv paper, Thank you. Now I found that the second wave in section 3.4 was not the proper 2nd solution of the free wave, a minus sign was missing. Oscillations were needed to force the traces to the mid plane. Now with an additional “near field” the field lines directly approach always clean simple circular tracks. This is demonstrated in my new version.
Hello Victor and Guenter,
A very good question.
I've proposed a model of the electron as a circulating charged photon that generates the de Broglie wavelength, which is a basis of the Schrodinger equation. You will find my work on ResearchGate, in particular my papers
https://www.researchgate.net/publication/272167387_The_Electron_is_a_Charged_Photon_with_the_de_Broglie_Wavelength
and
https://www.researchgate.net/publication/271077958_The_Charged-Photon_Model_of_the_Electron_Fits_the_Schrdinger_Equation
with best regards,
Richard
Article The Electron is a Charged Photon with the De Broglie Wavelength
Article The Charged-Photon Model of the Electron Fits the Schrödinger Equation
@Dr. Guenter Poelz and Richard Gauthier: thank you for your comments. I just wrote a new paper discussing linearised Einstein field equations, but touching also your wave model of electron. Your comments are welcome. Thanks
Article String without String: How Linearised Einstein’s Field Equat...
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