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Journal of Modern Physics

Emission Intensity in the Hydrogen Atom Calculated from a Non-Probabilistic Approach to the Electron Transitions

Stanisƚaw Olszewski

Published Jan 1, 2016• 15 citations
Publisher

Abstract

Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.

DOI
10.4236/jmp.2016.78076

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Quantum aspects of the Joule-Lenz law for the transmission of energy allowed us to calculate the time rate of energy transitions between the quantum states of the hydrogen atom in a fully non-probabilistic way. The calculation has been extended to all transitions between p and s states having main quantum numbers not exceeding 6. An evident similarity between the intensity pattern obtained from the Joule-Lenz law and the corresponding quantum-mechanical transition pro-babilities has been shown.
Definitions of the mechanical parameters entering the Bohr model of the hydrogen atom allowed us to calculate the time intervals connected with the electron transitions between the nearest-neighbouring energy levels in the atom. This is done in a strictly non-probabilistic way. The time results are compared with those derived earlier on the basis of the classical Joule-Lenz law for the energy emission adapted to the case of the electron transfer in the quantum systems. A similar formalism has been next applied to the harmonic oscillator and a particle moving in the one-dimensional potential box.
The Joule-Lenz law for a classical expense of energy is transformed into a formula representing a quantummechanical invariant composed of the interval of energy connected with an electron transition and the corresponding interval of transition time between two quantum levels.Time and energy enter the invariant formula on an equal footing, moreover the time intervals converge with the time periods characteristic for the examined quantum systems.These properties imply to consider the time intervals as quanta of time having character similar to that possessed by the energy.Another result of the transformation of the Joule-Lenz law is the time rate of energy of the quantum transitions.This rate is calculated on a fully non-probabilistic way.When examined for the hydrogen atomic spectrum taken as an example, the obtained quantum rate is by many orders larger than a classical transition rate.
The paper presents a non-probabilistic approach to the time interval associated with the energy emission produced by the electron transition in a quantum system. The calculations were performed for the hydrogen atom and the electron particle in a one-dimensional potential box. In both cases, the rule of conservation of the electron momentum has been applied. The results, limited to the time intervals of transitions between two neighbouring quantum energy levels, occur to be much similar to those obtained earlier with the aid of the Joule-Lenz energy emission theory.
The time of the energy emission between two neighbouring electron levels in the hydrogen atom has been calculated first on the basis of the quantum aspects of the Joule-Lenz law, next this time is approached with the aid of the electrodynamical parameters characteristic for the electron motion in the atom. Both methods indicate a similar result, namely that the time of emission is close to the time period of the electromagnetic wave produced in course of the emission. As a by-product of calculations, the formula representing the radius of the electron microparticle is obtained from a simple combination of the expressions for the Bohr magnetic moment and a quantum of the magnetic flux.
In the first step, the Joule-Lenz dissipation energy specified for the electron transitions between two neighbouring quantum levels in the hydrogen atom has been compared with the electromagnetic energy of emission from a single level. Both the electric and magnetic vectors entering the Pointing vector of the electromagnetic field are referred to the one-electron motion performed along an orbit in the atom. In the next step, a similar comparison of emission rates is performed for the harmonic oscillator. Formally a full agreement of the Joule-Lenz and electromagnetic expressions for the energy emission rates has been attained.