A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model

Thomas Allmendinger

doi:doi:10.11648/j.ijamtp.20160201.11

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A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model

Thomas Allmendinger

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 1)

Received: 13 June 2016 Accepted: 22 June 2016 Published: 1 August 2016

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Abstract

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.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 1)
DOI	10.11648/j.ijamtp.20160201.11
Page(s)	1-15
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Quantum-Mechanics, Uncertainty-Principle, Wave-Particle-Dualism, Three-Dimensional Electron-Trajectories, Electron-Oscillation, Resonance-Effect

References

[1]	Richard P. Feynman: „QED - The Strange Theory of Light and Matter”, Princeton 1985
[2]	Manjit Kumar: „Quantum, Einstein, Bohr and the Great Debate about the Nature of Reality”, Cambridge 2008. Deutsche Ausgabe: “Quanten”, Berlin 2009
[3]	Johann Jakob Balmer: „Notiz über die Spectrallinien des Wasserstoffs“, Ann. Phys. 261/5 (1885), 80-87
[4]	Albert Einstein: „Ueber einen die Erzeugung und Verwandlung des Lichts betreffenden heuristischen Gesichtspunkt“, Ann. Phys. 322/6 (1905)
[5]	Niels Bohr: „On the Constitution of Atoms and Molecules“, Philosoph. Magazine 26 (1913), 1-25
[6]	Arnold Sommerfeld: „Zur Quantentheorie der Spektrallinien”, Ann. Phys. 51 Vol. 356 (1916), 1-96
[7]	H. Mark u. R. Wierl: „Atomformfaktorbestimmung mit Elektronen“, Z. Phys. 60 (1930), 741-53
[8]	Gerhard Herzberg: „Atomic Spectra and Atomic Structure“, New York 1944, fig. 15 on p. 31
[9]	Amit Goswami: „Das bewusste Universum”, Lüchow-Verlag, Stuttgart 1997
[10]	Werner Heisenberg: „Über die quantentheoretische Um¬deutung kinematischer und mecha¬nischer Beziehungen“, Z. Phys. 33 (1925), 879-93
[11]	Erwin Schrödinger: „An undulatory theory of the mechanics of atoms and molecules“, Phys. Rev. 28 (1926), 104
[12]	Erwin Schrödinger: “Quantisierung als Eigenwertproblem” (1. Mitteilung), Ann. Phys. 79 Vol. 384/4 (1926), 361
[13]	Erwin Schrödinger: „Quantisierung als Eigenwertproblem” (2. Mitteilung), Ann. Phys. 79 Vol. 384/6 (1926), 32
[14]	Max Born und Pascual Jordan: „Zur Quantenmechanik“, Z. Phys. 34/1 (1925), 858-88
[15]	Max Born: „Zur Quantenmechanik der Stossvorgänge“, Z. Phys. 37/12 (1926), 863-67
[16]	Detlef Dürr and Stefan Teufel: „Bohemian Mechanics”, Springer 2009
[17]	Dieter Meschede: „Gerthsen Physik”, 21. völlig neu bear¬beite¬te Auflage, Springer 2001

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Thomas Allmendinger. (2016). A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model. International Journal of Applied Mathematics and Theoretical Physics, 2(1), 1-15. https://doi.org/10.11648/j.ijamtp.20160201.11

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Thomas Allmendinger. A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model. Int. J. Appl. Math. Theor. Phys. 2016, 2(1), 1-15. doi: 10.11648/j.ijamtp.20160201.11

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Thomas Allmendinger. A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model. Int J Appl Math Theor Phys. 2016;2(1):1-15. doi: 10.11648/j.ijamtp.20160201.11

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@article{10.11648/j.ijamtp.20160201.11,
  author = {Thomas Allmendinger},
  title = {A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {2},
  number = {1},
  pages = {1-15},
  doi = {10.11648/j.ijamtp.20160201.11},
  url = {https://doi.org/10.11648/j.ijamtp.20160201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20160201.11},
  abstract = {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.},
 year = {2016}
}

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TY  - JOUR
T1  - A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model
AU  - Thomas Allmendinger
Y1  - 2016/08/01
PY  - 2016
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DO  - 10.11648/j.ijamtp.20160201.11
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
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PB  - Science Publishing Group
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AB  - 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.
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Author Information

Thomas Allmendinger

Independent Scholar, Glattbrugg, Zurich, Switzerland

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Thomas Allmendinger. (2016). A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model. International Journal of Applied Mathematics and Theoretical Physics, 2(1), 1-15. https://doi.org/10.11648/j.ijamtp.20160201.11

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ACS Style

Thomas Allmendinger. A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model. Int. J. Appl. Math. Theor. Phys. 2016, 2(1), 1-15. doi: 10.11648/j.ijamtp.20160201.11

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AMA Style

Thomas Allmendinger. A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model. Int J Appl Math Theor Phys. 2016;2(1):1-15. doi: 10.11648/j.ijamtp.20160201.11

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@article{10.11648/j.ijamtp.20160201.11,
  author = {Thomas Allmendinger},
  title = {A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {2},
  number = {1},
  pages = {1-15},
  doi = {10.11648/j.ijamtp.20160201.11},
  url = {https://doi.org/10.11648/j.ijamtp.20160201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20160201.11},
  abstract = {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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - A Classical Approach to the De Broglie-Wave Based on Bohr’s H-Atom-Model
AU  - Thomas Allmendinger
Y1  - 2016/08/01
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20160201.11
DO  - 10.11648/j.ijamtp.20160201.11
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 1
EP  - 15
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20160201.11
AB  - 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.
VL  - 2
IS  - 1
ER  -

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