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Magnetic Moment of an Electron, it's Spin and de Broglie Oscillations.

Bezverkhniy Volodymyr Dmytrovych, Bezverkhniy Vitaliy Volodymyrovich.

Published Sep 1, 2019• 0 citations
OpenAlex

Abstract

Using the idea of de Broglie oscillations in elementary particles, for example, in an electron, it is easy to obtain quantitative values of the magnetic moment of an electron and the electron spin. Based on the oscillations the gyromagnetic ratio is logically explained. The calculations presented in the work once again confirm the reality of the existence of a periodic process in elementary particles, that is, de Broglie oscillations.

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Cambridge University Press eBooks•Jul 13, 2023•0 citations
Using the idea of de Broglie oscillations in elementary particles, for example, in an electron, it is easy to obtain quantitative values of the magnetic moment of an electron and the electron spin. Based on the oscillations the gyromagnetic ratio is logically explained. The calculations presented in the work once again confirm the reality of the existence of a periodic process in elementary particles, that is, de Broglie oscillations.
The De Broglie's approach to the quantum theory, when combined with the conservation rule of momentum, allows one to calculate the velocity of the electron transition from a quantum state n to its neighbouring state as a function of n.The paper shows, for the case of the harmonic oscillator taken as an example, that the De Broglie's dependence of the transition velocity on n is equal to the n-dependence of that velocity calculated with the aid of the uncertainty principle for the energy and time.In the next step the minimal distance parameter provided by the uncertainty principle is applied in calculating the magnetic moment of the electron which effectuates its orbital motion in the magnetic field.This application gives readily the electron spin magnetic moment as well as the quantum of the magnetic flux known in superconductors as its result.
The existence of an internal frequency associated to any elementary particle conjectured by de Broglie is compared with a classical description of the electron, where this internal structure corresponds to the motion of the centre of charge around the centre of mass of the particle. This internal motion has a frequency twice de Broglie's frequency, which corresponds to the frequency found by Dirac when analysing the electron structure. To get evidence of this internal electron clock a kind of experiment as the one performed by Gouanére et al. \cite{Gouanere} will show a discrete set of momenta at which a resonant scattering effect, appears. The resonant momenta of the electron beam are given by pk=161.748/kp_k=161.748/kpk​=161.748/k MeV/c/c/c, k=1,2,3,...k=1,2,3,...k=1,2,3,..., where only, the corresponding to k=2k=2k=2, was within the range of Gouanére et al. experiment. The extension of the experiment to other values of pkp_kpk​, would show the existence of this phenomenon.
Spin and helicityTraditionally, in textbooks on quantum mechanics, spin is introduced via an idealized Stern-Gerlach experiment in which a non-relativistic beam of silver atoms passes through an inhomogeneous magnetic field.Each atom is treated as a single valence electron of charge -e in an s-state.The subsequent splitting of the beam into two indicates the two-valuedness of Sz, which is related to the value 1/2 for s, and the magnitude of the splitting shows that the magnetic moment /l is related to s by e /l = -~s, me the proportionality factor (the gyromagnetic ratio) being twice as big as the factor that classically gives the magnetic moment due to the orbital angular momentum of a point charge.Historically, however, it seems that the early Stern-Gerlach experiments, begun in 1922, had no influence at all upon the discovery of spin, simply because they were too imprecise.Rather, the concept of spin appeared after a long and tedious battle to understand the splitting patterns and separations in line spectra.Several people had for various reasons discussed classical models of rotating charge distributions but Kronig, in 1924, was the first to show that an electron with spin 1/2 would explain the pattern of what we would today call L • S splitting, as well as anomalies in the Zeeman effect.He realized, though, that the gyromagnetic ratio ( -ejmc) needed for the latter would give L • S splittings twice as big as those observed.It is said that Pauli expressed his negative reaction to Kronig's idea with such vehemence that Kronig never published his work (Mehra and Rechenberg, 1982).Soon thereafter, in 1925, the same idea occurred to Uhlenbeck and Goudsmit (1925), who proceeded to a detailed analysis of the splittings, concluding at first that everything worked beautifully, but then becoming aware, as a consequence of a comment by Heisenberg, of the factor-of-2 inconsistency mentioned above.