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Australian Journal of Physics

Position Indeterminacy

Fosco Ruzzene

Published Mar 2, 2001• 2 citations
Publisher

Abstract

Calculations assuming position indeterminacy in the Dirac equation are reported.Energy shift contributions for low-lying states of hydrogen-like atoms are calculated by treating the position indeterminacy as a perturbation additional to standard quantum mechanics. The results are consistent with the current discrepancy between theory and experiment for Lamb shifts in hydrogen, deuterium and the helium ion.

DOI
10.1071/ph99076

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Calculations assuming position indeterminacy in the Dirac equation are reported.Energy shift contributions for low-lying states of hydrogen-like atoms are calculated by treating the position indeterminacy as a perturbation additional to standard quantum mechanics. The results are consistent with the current discrepancy between theory and experiment for Lamb shifts in hydrogen, deuterium and the helium ion.
In the literature of calculating atomic and molecular structures, most Schrodinger equations are described by Coulomb potential. However, there are also a few literatures that discuss some magnetic correction methods, such as Pauli and Shortley's early work. But in fact, the calculation accuracy of these Schrodinger equations is not consistent with Lamb shift. Therefore, in the traditional ab initio calculation of quantum mechanics, it is common and necessary to use Dirac theory or quantum electrodynamics (QED) to correct the energy level of Schrodinger equation. However, the calculation of Feynman diagram is a daunting problem, including the application of self-consistent field in relativity and density functional theory. So recently, we have noticed the simplicity of the modified Newtonian mechanics, and we think that quantum mechanics will have similar properties. Here, we state this and improve the correction function in our previous action potential. In addition, through the demonstration of hydrogen-like and helium-like systems here, it can be proved that this conclusion is a potential application, that is, the energy level structure of our modified Schrodinger equation is consistent with Lamb shift.
When the Dirac equation was first published in 1928, three solutions appeared immediately within the same year, each describing the most important problem in physics at that time: the hydrogen atom. These solutions lifted some of the degeneracy from earlier atomic models, but not all of it--they still predicted the same degenerate energy levels for the 2s1/2 and 2p1/2 states, for example. In this paper, we introduce a new solution of the Dirac equation, which finally removes all degeneracy from the hydrogen atom. We work in terms of dimensionless quantities and use the Lamb shift to give each atomic state in our model a unique, nondegenerate energy level. We obtain radial eigenfunctions in terms of the Laguerre polynomials, demonstrate how they can be reduced to the Schrodinger wavefunctions by applying limits, and plot our results.
In the scientific community dominates the conviction that the hydrogen atom is the simplest, and existing theories based on equations of Schrodinger and Dirac fully describe all the subtleties of behavior of an electron in a hydrogen atom. In this paper and in the following articles will be shown that in addition to the known state-based solutions of the Schrodinger and Dirac equations, there are states which were not studied and they were not known, or often simply were discarded with the phrase have no physical meaning. Further it will be shown that the existing equations of quantum mechanics, namely the Dirac equation, Klein-Gordon equation and especially the Schrodinger equation, can not accurately describe all the subtleties of behavior of an electron in a hydrogen atom. As a result there will be given a reasonable basis for the feasibility of an experimental search or targeted synthesis of new unknown states of the hydrogen atom.
The Bohr formulation—the original one—is now largely a matter of history. The usual career of a theory was its fate. It explained much, but it failed at the first signs of complication, even for the simplest molecules as hydrogen and helium. Some results were either only approximate in a loose or incomplete fashion, e.g. in the application of the correspondence principle to intensities, the only reliable predictions being only for an absence of certain lines, or they quite disagreed with experiment, e.g. in the case of the hydrogen molecule and the hydrogen molecule ion, the normal and excited states of helium, the anomalous Zeeman effect, the Ramsauer effect (the phenomenon of the deflection of electrons at low speeds being less than at higher speeds in atomic collisions), and in the treatment of problems where more than one electron was involved. In the last mentioned cases the perturbation method, so successful in solving “many-body” problems in celestial mechanics, failed completely because systems of several electrons, possessing frequencies of the order of light waves, cannot interact classically. A bit of much forced pragmatism was practiced in treating the many electron atom as a variation of the hydrogen atom. Besides, there were technical oddities, like ½ quantum numbers, and impenetrated anologies between visible and X-ray spectra.