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Electron Motion in Atoms-Classical Quantum Theory

Daehyeon Kang

Published Mar 1, 2020• 0 citations
OpenAlex

Abstract

We attempts to show what electron motion looks like in the S orbital of hydrogen atoms. by Classical quantum theory S-orbital is the case without angular momentum, which is natural in Schrodinger's equation but difficult to explain in classical quantum theory. Classical quantum theory is still valid even now, when quantum mechanics flourished.

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We attempts to show what electron motion looks like in the S orbital of hydrogen atoms. by Classical quantum theory S-orbital is the case without angular momentum, which is natural in Schrodinger's equation but difficult to explain in classical quantum theory. Classical quantum theory is still valid even now, when quantum mechanics flourished.
Even after extensive research in Quantum Mechanics, we are still unable to visualize instant-to-instant motion of an electron in hydrogen atom. That is because in QM treatment, potential energy term has been mistakenly assumed to be time-independent instead of depending on the instant-to-instant varying position of the orbiting electron [1]. This has led to wrong and weird solutions for the electron motion in hydrogen atom. Before the advent of wave mechanics, Sommerfeld model of elliptical electron orbits was able to explain most features of hydrogen spectra, except for the features associated with electron spin and magnetic moment interactions. However, the Sommerfeld elliptical orbits were of kinematic origin and could not provide visualization of instant-to-instant dynamic motion of the orbiting electron. Contrary to the QM perspective, we find that central core of the electron behaves as a classical particle while its electrostatic field behaves as a wave phenomenon. As such an electron under Coulomb force moves strictly in accordance with Newtonian laws of motion. In this paper, we develop dynamic electron orbits in hydrogen atom by using energy and angular momentum conservation principle in central force field. We have shown that during photon emission, angular momentum of the orbiting electron is changed by ħ due to recoil action. This may be the origin of various quantization rules. During emission of a photon, elliptical orbit transitions are also computed and plotted. Orbit transition time is of the order of 10-16 seconds. We have extended this methodology to compute electron orbits in hydrogen molecular bond and computed the H2 bond energy.
In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work, we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrödinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.
In view of difficulties and questions of quantum mechanics in description of motion of electrons in hydrogen atom, we here established their nonlinear theory of motion based on the true motions of electron and nucleon and the real interactions between them, in which the motion of electron is depicted by a nonlinear Schrödinger equation with a Coulomb potential, the nonlinear interaction b∣φ∣2φ is produced by the change of Coulomb interaction between nucleon and electron due to the motion of nucleon. Thus the natures of the electron are thoroughly changed relative to those in quantum mechanics due to the nonlinear interactions, it not only is stable and localized, but also possesses a wave–corpuscle duality. Meanwhile, if its eigenenergy is still quantized and distributed in accordance with the energy levels, then we can use the new theory to explain perfectly the spectrum features of hydrogen atom, which resembles quantum mechanics, but its sizes of eigenenergy are depressed relative to that in quantum mechanics. This means that the nonlinear interaction enhances the localized and stable nature of the electron. Therefore, the new nonlinear theory is successful and correct to the hydrogen atom.
In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the later cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrodinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.