The fine structure of Weber’s hydrogen atom: Bohr–Sommerfeld approach

The fine structure of Weber’s hydrogen atom: Bohr–Sommerfeld approach

In this paper, we determine in second order in the fine structure constant the energy levels of Weber’s Hamiltonian that admit a quantized torus. Our formula coincides with the formula obtained by Wesley using the Schrödinger equation for Weber’s Hamiltonian. We follow the historical approach of Som...

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Veröffentlicht in:Zeitschrift für angewandte Mathematik und Physik 2019-08, Vol.70 (4), p.1-12, Article 105
Hauptverfasser: Frauenfelder, Urs, Weber, Joa
Format: Artikel
Sprache:eng
Schlagworte:
Electrodynamics
Energy levels
Engineering
Fine structure
Mathematical Methods in Physics
Schrodinger equation
Theoretical and Applied Mechanics
Toruses
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Zusammenfassung:In this paper, we determine in second order in the fine structure constant the energy levels of Weber’s Hamiltonian that admit a quantized torus. Our formula coincides with the formula obtained by Wesley using the Schrödinger equation for Weber’s Hamiltonian. We follow the historical approach of Sommerfeld. This shows that Sommerfeld could have discussed the fine structure of the hydrogen atom using Weber’s electrodynamics if he had been aware of the at-his-time-already-forgotten theory of Wilhelm Weber (1804–1891).
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-019-1149-4