Quantum Invariants Descending from the Joule-Lenz Law for the Dissipated Energy Applied in Calculating the Rate of Electron Transitions

Abstract

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 de Broglie Waves and Joule-Lenz Law Applied in Examining the Electron Transitions in Small Quantum Systems

“…This property allows us to consider also transitions in which the number of participating objects is relatively small. Moreover, when the Joule-Lenz classical approach [3] is applied on the quantum footing [4], the intensity of the energy emission can be estimated for a transition of a single particle without any reference to the probabilistic theory.In effect, the aim of the present paper became to examine a single electron transition in small quantum systems on both probabilistic and non-probabilisticfooting. An analysis of the classical physical parameters of mechanics, thermodynamics and electrodynamics which can be connected with the transition seems to be then of use.…”

“…This property allows us to consider also transitions in which the number of participating objects is relatively small. Moreover, when the Joule-Lenz classical approach [3] is applied on the quantum footing [4], the intensity of the energy emission can be estimated for a transition of a single particle without any reference to the probabilistic theory.…”