Quantum Physics

    

De Broglie's Phase Waves of Electrons in Hydrogen-Like Atoms as Parts of Steady-State Forced Vibrations

Authors: Martin Kraus

One of the consequences of de Broglie's hypothetical internal clock of an electron is the existence of an associated phase wave that is locally in phase with the electron's internal clock. For a classical electron that is moving on a closed Bohr-Sommerfeld orbit in the electric potential of a positively charged nucleus, de Broglie showed that the requirement of a continuous phase wave on the closed orbit is in agreement with Einstein's quantization condition. The present work explores the hypothesis that this phase wave is part of a forced vibration in the space around the nucleus, which is driven by the electron's internal clock. Results of this work include new quantization conditions for closed orbits that are consistent with Einstein's quantization condition but include additional (yet unexplored) conditions. Furthermore, a method is presented for computing phase waves on closed orbits of electrons, which could help visualizing several important features of de Broglie's phase waves.

Comments: 7 Pages. This revision fixes typos and adds a reference; full list of changes in the paper.

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[v1] 2025-03-02 18:29:06
[v2] 2025-07-10 13:22:03

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