Old Quantum Mechanics by Bohr and Sommerfeld from a Modern Perspective
Quantum Physics
2026-03-04 v6 History and Philosophy of Physics
Abstract
We review Bohr's atomic model and its extension by Sommerfeld from a mathematical perspective of wave mechanics. The derivation of quantization rules and energy levels is revisited using semiclassical methods. Sommerfeld-type integrals are evaluated by elementary techniques, and connections with the Schr\"{o}dinger and Dirac equations are established. Historical developments and key transitions from classical to quantum theory are discussed to clarify the structure and significance of the old quantum mechanics.
Keywords
Cite
@article{arxiv.2506.00408,
title = {Old Quantum Mechanics by Bohr and Sommerfeld from a Modern Perspective},
author = {Kamal K. Barley and Andreas Ruffing and Sergei K. Suslov},
journal= {arXiv preprint arXiv:2506.00408},
year = {2026}
}
Comments
37 pages, 8 figures, 93 references