American Journal of Modern Physics

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An Algebraic Operator Approach to Aharonov-Bohm Effect

Received: 31 January 2015    Accepted: 13 February 2015    Published: 26 February 2015
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Abstract

A new approach based on algebraic quantum operator, is pursued in order to investigate the Aharonov-Bohm effect. Introducing a SU(2) dynamical invariance algebra, the discrete spectrum and the energy level of the quantum Aharonov-Bohm effect is obtained. This alternative method will help undergraduate students to broader their knowledge about this interesting quantum phenomenon.

DOI 10.11648/j.ajmp.20150402.12
Published in American Journal of Modern Physics (Volume 4, Issue 2, March 2015)
Page(s) 44-49
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 Physics, Schrödinger Equation, Spherical Coordinates, Hyperbolic Coordinates, Aharonov-Bohm Effect, Operator

References
[1] S. Gasiorowicz: Quantum physics, John Wiley (1974)
[2] Y. Aharonov, D. Bohm: Physical Review 115: 485–91 (1959)
[3] L. Page: Physical Review 36, 444 (1930)
[4] A. Batelaan, A. Tonomura: Physics Today 62 (9): 38-43 (2009)
[5] E. Sjöqvist: Physical Review Letters 89 (21): 210401 (2002)
[6] W. Ehrenberg, R.E. Siday: Proceedings of the Physical Society. Series B 62: 8–21 (1949)
[7] F.D. Peat: Infinite Potential: The Life and Times of David Bohm, Addison-Wesley. ISBN 0-201-40635-7 (1997)
[8] Y. Aharonov, D. Bohm: Physical Review 123: 1511–1524 (1961)
[9] M. Peshkin, A. Tonomura: The Aharonov–Bohm effect. Springer-Verlag. ISBN 3-540-51567-4 (1989)
[10] L. Vaidman: Physical Review A 86 (4): 040101 (2012)
[11] R. Feynman: The Feynman Lectures on Physics 2, pp. 15–5 (1964)
[12] V.Y. Chernyak, N.A. Sinitsyn: Journal of Chemical Physics 131(18): 181101 (2009)
[13] H.D. Doebner, E. Papp: Physics Letters A 144, 8–9, Pages 423–426 (1990)
[14] Gh. E. Draganascu, C. Campigotto, M. Kibler: Physics Letters A 170, 6, 339–343 (1992)
[15] M. Kibler, C. Campigotto: Physics Letters A 181, 1, 1–6 (1993)
[16] M. R. Brown, B. J. Hiley: arXiv:quant-ph/0005026v5
[17] S. Sakoda, M. Omote: Advances in Imaging and Electron Physics 1, 110, 101–171 (1999)
[18] M. Aktaş: International Journal of Theoretical Physics 48, 7, 2145–2163 (2009)
[19] M. Aktaş: Journal of Mathematical Chemistry 49, 9, 1831–1842 (2011)
[20] E. Jung, M-R. Hwang, C-S. Park, D. Park: Journal of Physics A: Mathematical and Theoretical 45, 5, 055301 (2012)
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  • APA Style

    Farrin Payandeh. (2015). An Algebraic Operator Approach to Aharonov-Bohm Effect. American Journal of Modern Physics, 4(2), 44-49. https://doi.org/10.11648/j.ajmp.20150402.12

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    ACS Style

    Farrin Payandeh. An Algebraic Operator Approach to Aharonov-Bohm Effect. Am. J. Mod. Phys. 2015, 4(2), 44-49. doi: 10.11648/j.ajmp.20150402.12

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    AMA Style

    Farrin Payandeh. An Algebraic Operator Approach to Aharonov-Bohm Effect. Am J Mod Phys. 2015;4(2):44-49. doi: 10.11648/j.ajmp.20150402.12

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  • @article{10.11648/j.ajmp.20150402.12,
      author = {Farrin Payandeh},
      title = {An Algebraic Operator Approach to Aharonov-Bohm Effect},
      journal = {American Journal of Modern Physics},
      volume = {4},
      number = {2},
      pages = {44-49},
      doi = {10.11648/j.ajmp.20150402.12},
      url = {https://doi.org/10.11648/j.ajmp.20150402.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20150402.12},
      abstract = {A new approach based on algebraic quantum operator, is pursued in order to investigate the Aharonov-Bohm effect. Introducing a SU(2) dynamical invariance algebra, the discrete spectrum and the energy level of the quantum Aharonov-Bohm effect is obtained. This alternative method will help undergraduate students to broader their knowledge about this interesting quantum phenomenon.},
     year = {2015}
    }
    

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Author Information
  • Department of Physics, Payame Noor University (PNU), P.O. BOX, 19395-3697 Tehran, Iran

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