History and Philosophy of Physics

   

Remarks on the Non-Relativistic Bohr-Sommerfeld Model with Corrected Orbital Angular Momentum

Authors: Martin Kraus

Since the 1930s, a correction to the non-relativistic Bohr-Sommerfeld model of hydrogen-like atoms has been known, which aligns many predictions of this model with the predictions of the non-relativistic spinless Schrödinger equation for hydrogen-like atoms. In particular, the orbital angular momentum of electronic orbits in the corrected Bohr-Sommerfeld model match the orbital angular momentum of the corresponding single-electron wave functions that solve the mentioned Schrödinger equation. However, the only known justification for this correction has been the improvement of the predictions of the Bohr-Sommerfeld model. The present remarks revisit this correction in the context of a recently proposed vibrational interpretation of the Schrödinger equation, which provides a physical reason for this correction. Furthermore, numerical results are presented that support a previously hypothesized relation between nodal patterns in single-electron wave functions and corresponding de Broglie-wave-analyzed orbits provided that the mentioned correction is employed.

Comments: 4 Pages.

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[v1] 2026-10-25 14:01:16

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