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Photonics

Orbital and Spin Dynamics of Electron’s States Transition in Hydrogen Atom Driven by Electric Field

Ciann‐Dong Yang, Shiang-Yi Han

Published Sep 2, 2022• 1 citation
Publisher

Abstract

State transition in the multiple-levels system has the great potential applications in the quantum technology. In this article we employ a deterministic approach in complex space to analyze the dynamics of the 1s-2p electron transition in the hydrogen atom. The electron’s spin motion is embodied in the framework of quantum Hamilton mechanics that allows us to examine the transition dynamics more precisely. The transition is driven by an oscillating electric field in the z-direction. The electron’s transition process can be visualized by monitoring its motion in the complex space. The quantum potential and the total energy proposed in this paper provide new indices to observe the dynamic changes of electrons in the transition process.

DOI
10.3390/photonics9090634

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State transition in the multiple-levels system has the great potential applications in the quantum technology. In this article we employ a deterministic approach in complex space to analyze the dynamics of the 1s-2p electron transition in the hydrogen atom. The electron’s spin motion is embodied in the framework of quantum Hamilton mechanics that allows us to examine the transition dynamics more precisely. The transition is driven by an oscillating electric field in the z-direction. The electron’s transition process can be visualized by monitoring its motion in the complex space. The quantum potential and the total energy proposed in this paper provide new indices to observe the dynamic changes of electrons in the transition process.
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.
Based solely on internationally recognized laboratory measured data of the ground-state hydrogen atom, this paper conducts complete calculation and logical derivation of the whole process of electron orbital motion. The whole process includes all core parameters and derivation processes, such as orbital circumference, revolutions per second, equivalent plane square calculation of flattened spherical surface, total number of orbital positions and spatial traversal times, abandoning all subjective assumptions and complex solid geometry disputes. The research clearly shows that the electron has a unique and fixed orbital position at every moment, without quantum superposition state or spontaneous transition. The so-called electron cloud is only the trajectory coverage effect formed by the ultra-high-speed motion of electrons; the so-called quantum superposition state and quantum transition are both misunderstandings of classical deterministic orbital motion. Based on measured data, this paper negates the core hypotheses of electron cloud, superposition state and quantum transition in quantum mechanics with verifiable calculation and logic, proving that electrons are always in deterministic orbital motion, and the stability of atoms is completely governed by classical mechanical rules.
The de Broglie–Bohm causal theory of quantum mechanics with spin-dependence is used to determine electron trajectories when a hydrogen atom is subjected to (semiclassical) radiation. The transition between the 1s ground state and the 2p 0 state is examined. It is found that transitions can be identified along Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of revolution in R 3 . The energy along the trajectories is also discussed in relation to the hydrogen energy eigenvalues.
In the first step, the Ehrenfest reasoning concerning the adiabatic invariance of the angular orbital momentum is applied to the electron motion in the hydrogen atom. It is demonstrated that the time of the energy emission from the quantum level n+1 to level n can be deduced from the orbital angular momentum examined in the hydrogen atom. This time is found precisely equal to the time interval dictated by the Joule-Lenz law governing the electron transition between the levels n+1 and n. In the next step, the mechanical parameters entering the quantum systems are applied in calculating the time intervals characteristic for the electron transitions. This concerns the neighbouring energy levels in the hydrogen atom as well as the Landau levels in the electron gas submitted to the action of a constant magnetic field.
The mechanical angular momentum and magnetic moment of the electron and proton spin have been calculated semiclassically with the aid of the uncertainty principle for energy and time.The spin effects of both kinds of the elementary particles can be expressed in terms of similar formulae.The quantization of the spin motion has been done on the basis of the old quantum theory.It gives a quantum number n = 1/2 as the index of the spin state acceptable for both the electron and proton particle.In effect of the spin existence the electron motion in the hydrogen atom can be represented as a drift motion accomplished in a combined electric and magnetic field.More than 18,000 spin oscillations accompany one drift circulation performed along the lowest orbit of the Bohr atom.The semiclassical theory developed in the paper has been applied to calculate the doublet separation of the experimentally well-examined D line entering the spectrum of the sodium atom.This separation is found to be much similar to that obtained according to the relativistic old quantum theory.
In quantum mechanics, the only known quantitative index describing a state transition process is the occupation probability. In this paper, we propose three new quantitative indices, namely, complex transition trajectory, quantum potential, and total quantum energy, to give an elaborate description of state-transition behavior, which otherwise cannot be manifested in terms of occupation probability. The new quantitative indices and the nonlinear dynamics governing quantum transition behavior are derived from the quantum Hamilton mechanics that provides a unified description of the entire transition process from an initial state to a final state via an entangled state. The proposed nonlinear analysis of transition behavior will be applied to the transition in a hydrogen atom from the 1s state to the 2s state. Introduction of complex mechanics In conventional quantum mechanics (QM), a particle’s position and momentum in a quantum system can only be obtained in terms of an expectation value through a quantum operator. To reflect this situation, one can imagine that there is a bee in a house with no window. Suppose that the bee has a