A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model
International Journal of Applied Mathematics and Theoretical Physics
Volume 2, Issue 1, January 2016, Pages: 1-15
Received: Jun. 13, 2016; Accepted: Jun. 22, 2016; Published: Aug. 1, 2016
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Thomas Allmendinger, Independent Scholar, Glattbrugg, Zurich, Switzerland
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The atom model of Niels Bohr is commonly considered as antiquated even if it describes the atomic spectrum of hydrogen quite accurately. The later published relation of Louis De Broglie could arithmetically be implemented into Bohr’s formulation, leading to the concept of standing waves as the existence cause of excited electron states. However, at that time it was not possible to find well defined electron trajectories being classically describable. As a consequence, the »quantum mechanics« were developed by several authors, particularly by Schrödinger and by Heisenberg, but delivering a hardly under¬standable formalism where the classical physical laws appear being abrogated while abstract terms replace concrete and imaginable ones, abandoning the particle perception of mass points. In particular, Heisenberg’s »uncertainty principle« and the assumption of state probabilities seem to be in a striking variance to the idea of standing waves. In contrast, a formulation is given here which exactly describes the electron trajectories in the exited states solely by applying classical physical laws. Firstly, the original Bohr-model - in combination with De Broglie’s relation - is rolled up. From this formula system a vibration frequency - corresponding to the De-Broglie frequency – is deduced which is n-times larger than the rotation frequency of the Bohr-model. Furthermore, a direct coherence between that vibration-frequency of the electron and the frequency of the involved light is evident being explainable as a resonance effect. Then, a three-dimensional model is proposed where the electron oscillates and pulses perpendicularly to a virtual rotation plane i.e. rotating around a vertical axis, accompanied by a perpetual energy exchange between potential and kinetic energy. This leads at the excited, metastable energy states to well-defined, three-dimensional and wavy trajectories winding up on a surface similar to the one of a hyperboloid, whereas at the ground state the trajectory is planar and stable.
Quantum-Mechanics, Uncertainty-Principle, Wave-Particle-Dualism, Three-Dimensional Electron-Trajectories, Electron-Oscillation, Resonance-Effect
To cite this article
Thomas Allmendinger, A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model, International Journal of Applied Mathematics and Theoretical Physics. Vol. 2, No. 1, 2016, pp. 1-15. doi: 10.11648/j.ijamtp.20160201.11
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This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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