Quantum Invariants Descending from the Joule-Lenz Law for the Dissipated Energy Applied in Calculating the Rate of Electron Transitions
S. Olszewski
Institute of Physical Chemistry, Polish Academy of Sciences, M. Kasprzaka 44/52, 01-224 Warsaw, Poland
Received: January 8, 2016; In final form: January 2, 2017
Full Text PDF
The Joule-Lenz law for a classical expense of energy is transformed into a formula representing a quantum-mechanical 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.

DOI: 10.12693/APhysPolA.131.226
PACS numbers: 03.65.-w, 03.65.Sq