Open AccessSome arguments for the wave equation in Quantum theory
Author(s) -
Tristram de Piro,
AUTHOR_ID
Publication year - 2021
Publication title -
open journal of mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 2616-4906
pISSN - 2523-0212
DOI - 10.30538/oms2021.0168
Subject(s) - electromagnetic field , maxwell's equations , wave equation , inertial frame of reference , stability (learning theory) , charge (physics) , physics , mathematics , classical mechanics , series (stratigraphy) , field (mathematics) , mathematical analysis , quantum mechanics , pure mathematics , computer science , paleontology , machine learning , biology
We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.