V.6 No 1 
43 
On the waveparticle duality 

On the waveparticle duality S. B. Karavashkin and O.N. Karavashkina Special Laboratory for Fundamental Elaboration SELF 187 apt., 38 bldg., Prospect Gagarina, Kharkov, 61140, Ukraine phone +38 (057) 7370624; email: selftrans@yandex.ru , selflab@mail.ru
Abstract We will study the phenomena of interference and diffraction of electrons from the point of modelling of processes, basing on the quantummechanical and classical approaches. We will reveal that when we represent an electron as some wave function of state or of probability of location in some region of space, it causes considerable contradictions producing the waveparticle duality and incorrect description of the phenomenon. In particular, probabilistic representation of wave function by Born leads to the fact that such probabilistic distribution has to exist also when electrons do not interact with atoms. The probabilistic model premises only positive values of probability, while the wave function is bipolar, which additionally distorts the idea of properties of electron. We will establish that the cause, why in the quantummechanical representation the model is distorted, is that in frames of this formalism the orbital motion of exterior electrons of atom is neglected and, consequently, the field of atom is taken stationary. Then interacting electrons have to have some spectrum of frequencies to interact in resonance with the atom according to the Schroedinger equation. This last causes full distortion of the wave function of electron and factually cancels the spectrum of frequencies and as a consequence the electron must turn into an EM wave of some resonance frequency. As an alternative to this representation, we will model the electron’s interaction with atom from the point of classical physics. In this model the field of atom will be represented as a field of skeleton and the field of the exterior orbital electron, due to which the resulting field becomes dynamic in the near of atom. Basing on the calculated dynamic field, we will model the interaction of the chain of electrons with this field and reveal that electrons form the periodic structure with the wavelength proportional to the product of period of orbiting of orbital electron into the velocity of interacting electrons. This wavelike formation propagates from the region of interaction within some angle, gradually changing its shape because of difference of velocities of the electrons after their interaction with the atom. The electrons in this set propagate according to the Rutherford model of scattering with account of the phase of dynamic field of the atom. The superimposition of many such wavelike formations causes the interference and diffraction patterns like the patterns of Xrays. This model will fully lift the waveparticle problem together with the discrepancies inherent in the quantummechanical formalism. Key words: quantum mechanics, waveparticle duality, electron diffraction on atom, charge waves Classnames by MSC 2000: 78A20, 78A45, 78M10, 81V45, 81V80, 81T80 Classnames by PASC 2001: 03.65.Nk, 03.65.w, 03.75.Dg
1. Introduction The problem considered in this paper arose on the edge of 20th century, when the diffraction and interference patterns were produced with the electrons passing through the crystal structures, and these patterns coincided with similar patterns of rays of light and with mechanical vibrations in continua in their interference and diffraction on the barriers. This caused the discrepancy in the corpuscular understanding of particles and the idea of particles as the de Broglie waves which originated then. “The de Broglie hypothesis has been brilliantly justified experimentally. Specifically, it was shown that the beams of electrons, protons and even integer atoms reveal the phenomena of interference absolutely same as the light and Xrays” [1, p. 444]. “Due to Davisson and Germer (1927) studies, it was established that in reflection of electron beams from metals, there take place the deviations from the pattern which the classical theory predicts: the number of electrons reflected in some directions appears more and in some other – less than expected, so we can speak of some kind of selected reflection at definite angles. In 1925 Elsasser put forward the hypothesis that we deal here with diffraction of electron waves on the lattice of metals – effect resembling the diffraction of Xrays in crystals. … The accurate experiments undertaken then by Davisson and Germer have really revealed the interference of electrons. The phenomenon in its form appeared fully similar to the known interference of Xrays” [2, p. 112]. The inversion in the date of Davisson and Germer’s experiment and date when Elsasser has put forward his hypothesis can be explained so: “Factually, interference of electron beams in crystals has been discovered before the de Broglie theory. In 1921 – 1923 Davisson and Kansmann found that in scattering of electrons by thin metal sheets there is observed a distinctive dependence of intensity on the scattering angle (see Fig. 1). With it, the location and value of maximums essentially depend on the velocity of electrons. An occasional circumstance showed the crucial part of crystal structure in this phenomenon: when experimenting with reflection from nickel plates, the glass instrument has cracked and the nickel plate has been oxidised. To reduce this plate, we had to roast it long time in vacuum and in hydrogen. After this, the plate encountered the recrystallisation: some quantity of large crystals has formed in it. When repeating the experiments with scattering of electrons, it appeared that due to this recrystallisation the pattern has abruptly changed: the number of maximums strongly grew and the maximums became well more distinctive (see Fig. 1)” [1, p. 445–446].

a 
b 
Fig. 1. Scattering of electrons by a polycrystalline plate: a – before roasting, b – after roasting

“The experiments to obtain the electronograms of the Debye type have been first successfully made by Thompson with the fast electrons (17 500 – 56 500 eV) and by P.S. Tarkovsky – with relatively slow electrons (up to 1 700 eV).

a b 
Fig. 2. The electronogram of thin sheets of gold (a) and copper (b) (Fig. 216, 217 from Shpolsky [1, p. 455] – Authors)

In Fig. 2 we show two images obtained with the sheets of gold and copper. As we can see, in both cases they produce typical rings of interference. We can show in a very simple way that these rings are produced by the very scattered electrons, not by the secondary Xrays: when turning on the magnetic field, the whole interference pattern shifts and distorts, while the interference pattern of Xrays remains unchanged, of course” [1, p. 455]. At the same time, there is also a considerable difference in the interference patterns produced by optic rays and electrons of which we mentioned in the beginning of Introduction. If two converged coherent rays of light are able to produce the interference pattern in absence of some barriers and modulators, two converged rays of electrons will not give this pattern. 
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