Classical Electromagnetic Derivation of the Bohr Spectrum
Abstract
Classical electrodynamics including Lorentz-invariant classical electromagnetic zero-point radiation leads to a ground state and resonant excited states for a charged particle in a Coulomb potential. These resonant states correspond to integer values of the action variables analogous to those appearing in the Bohr theory of the hydrogen atom. Thus there is a purely classical electromagnetic derivation of the Bohr energy levels. According to classical electromagnetic theory, it is not that there are states where the charged particle does not radiate, but rather in these states there is a resonant balance between radiation emission and absorption The work on classical zero-point radiation reported here is a continuation of the analysis published in 1975, but with the addition of the ideas of relativity and resonance between the charged-particle orbit and classical zero-point radiation.
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BibTeX
@misc{boyer2026classical,
title = {{Classical Electromagnetic Derivation of the Bohr Spectrum}},
author = {Timothy H. Boyer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23813},
eprint = {2609.23813},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23813},
}
RIS
TY - UNPB
TI - Classical Electromagnetic Derivation of the Bohr Spectrum
AU - Timothy H. Boyer
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23813
UR - https://arxiv.org/abs/2609.23813
AB - Classical electrodynamics including Lorentz-invariant classical electromagnetic zero-point radiation leads to a ground state and resonant excited states for a charged particle in a Coulomb potential. These resonant states correspond to integer values of the action variables analogous to those appearing in the Bohr theory of the hydrogen atom. Thus there is a purely classical electromagnetic derivation of the Bohr energy levels. According to classical electromagnetic theory, it is not that there are states where the charged particle does not radiate, but rather in these states there is a resonant balance between radiation emission and absorption The work on classical zero-point radiation reported here is a continuation of the analysis published in 1975, but with the addition of the ideas of relativity and resonance between the charged-particle orbit and classical zero-point radiation.
ER -