Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium

Oleg Olkhov

doi:doi:10.11648/j.ajpa.20140205.12

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Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium

Oleg Olkhov

Published in American Journal of Physics and Applications (Volume 2, Issue 5)

Received: 23 September 2014 Accepted: 21 October 2014 Published: 30 October 2014

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Abstract

The hypothesis was earlier suggested by the author where all micro-objects are considered as specific distortions of the physical space-time pseudo-Euclidean geometry, namely, as closed topological 4-manifolds. The foundation of the hypothesis is a geometrical interpretation of the basic equation of quantum mechanics for classical (not quantized) wave fields -- the Dirac equation for free particle. Such hypothesis does not contradict to any physical laws and experimental facts and gives firstly an opportunity to explain qualitatively within classical notions (geometrical) the so called “paradoxical” properties of quantum particles such as wave-corpuscular duality, appearance of probabilities in the quantum mechanics formalism, spin, EPR-paradox.To demonstrate prospects for suggested geometrical approach the author early attempted to find new dynamic equations other than known quantum-mechanical ones for atomic spectra calculations. In this work above investigation is being continued on a more rigorous basis, representing a new geometrical interpretation of the equation for hydrogen atoms. Results of calculations of ionization potentials for helium atom are in agreement with experimental data.

Published in	American Journal of Physics and Applications (Volume 2, Issue 5)
DOI	10.11648/j.ajpa.20140205.12
Page(s)	108-112
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), 2014. Published by Science Publishing Group

Keywords

Geometrical Interpretation, Quantum Mechanics, Atomic Spectra, Helium Spectrum

References

[1]	O. A. Olkhov, “Geometrical approach to the atomic spectra theory. The helium atom,” Russian J.of Phys.Chemistry B, vol. 8, pp.30—42, February 2014 [Chim.Fis., p.36, vol.33, №2, 2014].
[2]	O. A. Olkhov, “Geometrization of Quantum Mechanics,” Journal of Rhys.:Conf.Ser. vol. 67, p.012037. 2007.
[3]	O. A. Olkhov, “Geometrization of Classical Wave fields,” Mellwill, Ney York, AIP Conference Proceedings p. 316, vol.962,2008(Proc.Int.Conf,“Quantum theory: Reconsideration of Foundations, Vaxjo, Sweden, 11-16 June, 2007, 2007); arXiv: 802.2269
[4]	L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics. vol.4: V. B. Berestetzki, E. M. Lifshitz, L. P. Pitaevski, Quantum Electrodynamics, Butterworth-Heinemann, 1982.
[5]	B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern geometry—Methods and Applications, Part 2: The Geometry and Topology of Manifolds, Springer, 1985.
[6]	A. S. Schwartz, Quantum field theory and topology. Grundlehren der Math. Wissen.307, Springer, 1993.
[7]	H. S. M. Coxeter, Introduction to geometry. New York, London: John Wiley&Sons, 1961.
[8]	P. K. Rashevski, Riemann geometry and tensor analysis (in Russian). Moscow, Nauka, 1966.
[9]	V. A. Zelnorovich, Theory of spinors and its applications (in Russian). Moscow, August-Print, 2001.
[10]	Ta-Pei Cheng, Ling-Fong Li, Gauge theory of elementary particle physics. Clarendon Press, Oxford, 1984.
[11]	V. Popov, N. Konopleva, Gauge fields. Gordon and Breach Publishing Group, 1982.
[12]	H. A. Bethe and E. E. Salpeter, Quantum mechanics of one- and two-electron atoms. Berlin-Gottingen-Heidelberg, Springer-Verlag, 1957.
[13]	V. Heine, Group theory in quantum mechanics. London-Oxford-New York-Paris, Pergamon Press, 1960.
[14]	L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics, vol.2, L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, Butterworth—Heinemann, 1975.

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Oleg Olkhov. (2014). Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium. American Journal of Physics and Applications, 2(5), 108-112. https://doi.org/10.11648/j.ajpa.20140205.12

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Oleg Olkhov. Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium. Am. J. Phys. Appl. 2014, 2(5), 108-112. doi: 10.11648/j.ajpa.20140205.12

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Oleg Olkhov. Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium. Am J Phys Appl. 2014;2(5):108-112. doi: 10.11648/j.ajpa.20140205.12

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@article{10.11648/j.ajpa.20140205.12,
  author = {Oleg Olkhov},
  title = {Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium},
  journal = {American Journal of Physics and Applications},
  volume = {2},
  number = {5},
  pages = {108-112},
  doi = {10.11648/j.ajpa.20140205.12},
  url = {https://doi.org/10.11648/j.ajpa.20140205.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20140205.12},
  abstract = {The hypothesis was earlier suggested by the author where all micro-objects are considered as specific distortions of the physical space-time pseudo-Euclidean geometry, namely, as closed topological 4-manifolds. The foundation of the hypothesis is a geometrical interpretation of the basic equation of quantum mechanics for classical (not quantized) wave fields -- the Dirac equation for free particle. Such hypothesis does not contradict to any physical laws and experimental facts and gives firstly an opportunity to explain qualitatively within classical notions (geometrical) the so called “paradoxical” properties of quantum particles such as wave-corpuscular duality, appearance of probabilities in the quantum mechanics formalism, spin, EPR-paradox.To demonstrate prospects for suggested geometrical approach the author early attempted to find new dynamic equations other than known quantum-mechanical ones for atomic spectra calculations. In this work above investigation is being continued on a more rigorous basis, representing a new geometrical interpretation of the equation for hydrogen atoms. Results of calculations of ionization potentials for helium atom are in agreement with experimental data.},
 year = {2014}
}

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TY  - JOUR
T1  - Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium
AU  - Oleg Olkhov
Y1  - 2014/10/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajpa.20140205.12
DO  - 10.11648/j.ajpa.20140205.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 108
EP  - 112
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20140205.12
AB  - The hypothesis was earlier suggested by the author where all micro-objects are considered as specific distortions of the physical space-time pseudo-Euclidean geometry, namely, as closed topological 4-manifolds. The foundation of the hypothesis is a geometrical interpretation of the basic equation of quantum mechanics for classical (not quantized) wave fields -- the Dirac equation for free particle. Such hypothesis does not contradict to any physical laws and experimental facts and gives firstly an opportunity to explain qualitatively within classical notions (geometrical) the so called “paradoxical” properties of quantum particles such as wave-corpuscular duality, appearance of probabilities in the quantum mechanics formalism, spin, EPR-paradox.To demonstrate prospects for suggested geometrical approach the author early attempted to find new dynamic equations other than known quantum-mechanical ones for atomic spectra calculations. In this work above investigation is being continued on a more rigorous basis, representing a new geometrical interpretation of the equation for hydrogen atoms. Results of calculations of ionization potentials for helium atom are in agreement with experimental data.
VL  - 2
IS  - 5
ER  -

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Author Information

Oleg Olkhov

Institute of Chemical Physics, Moscow, Russia

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APA Style

Oleg Olkhov. (2014). Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium. American Journal of Physics and Applications, 2(5), 108-112. https://doi.org/10.11648/j.ajpa.20140205.12

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ACS Style

Oleg Olkhov. Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium. Am. J. Phys. Appl. 2014, 2(5), 108-112. doi: 10.11648/j.ajpa.20140205.12

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AMA Style

Oleg Olkhov. Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium. Am J Phys Appl. 2014;2(5):108-112. doi: 10.11648/j.ajpa.20140205.12

Copy | Download

@article{10.11648/j.ajpa.20140205.12,
  author = {Oleg Olkhov},
  title = {Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium},
  journal = {American Journal of Physics and Applications},
  volume = {2},
  number = {5},
  pages = {108-112},
  doi = {10.11648/j.ajpa.20140205.12},
  url = {https://doi.org/10.11648/j.ajpa.20140205.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20140205.12},
  abstract = {The hypothesis was earlier suggested by the author where all micro-objects are considered as specific distortions of the physical space-time pseudo-Euclidean geometry, namely, as closed topological 4-manifolds. The foundation of the hypothesis is a geometrical interpretation of the basic equation of quantum mechanics for classical (not quantized) wave fields -- the Dirac equation for free particle. Such hypothesis does not contradict to any physical laws and experimental facts and gives firstly an opportunity to explain qualitatively within classical notions (geometrical) the so called “paradoxical” properties of quantum particles such as wave-corpuscular duality, appearance of probabilities in the quantum mechanics formalism, spin, EPR-paradox.To demonstrate prospects for suggested geometrical approach the author early attempted to find new dynamic equations other than known quantum-mechanical ones for atomic spectra calculations. In this work above investigation is being continued on a more rigorous basis, representing a new geometrical interpretation of the equation for hydrogen atoms. Results of calculations of ionization potentials for helium atom are in agreement with experimental data.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Geometrical Approach in Atomic Physics: Atoms of Hydrogen and Helium
AU  - Oleg Olkhov
Y1  - 2014/10/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajpa.20140205.12
DO  - 10.11648/j.ajpa.20140205.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 108
EP  - 112
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20140205.12
AB  - The hypothesis was earlier suggested by the author where all micro-objects are considered as specific distortions of the physical space-time pseudo-Euclidean geometry, namely, as closed topological 4-manifolds. The foundation of the hypothesis is a geometrical interpretation of the basic equation of quantum mechanics for classical (not quantized) wave fields -- the Dirac equation for free particle. Such hypothesis does not contradict to any physical laws and experimental facts and gives firstly an opportunity to explain qualitatively within classical notions (geometrical) the so called “paradoxical” properties of quantum particles such as wave-corpuscular duality, appearance of probabilities in the quantum mechanics formalism, spin, EPR-paradox.To demonstrate prospects for suggested geometrical approach the author early attempted to find new dynamic equations other than known quantum-mechanical ones for atomic spectra calculations. In this work above investigation is being continued on a more rigorous basis, representing a new geometrical interpretation of the equation for hydrogen atoms. Results of calculations of ionization potentials for helium atom are in agreement with experimental data.
VL  - 2
IS  - 5
ER  -

Copy | Download