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Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model

Received: 23 November 2016     Accepted: 21 January 2017     Published: 24 February 2017
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Abstract

In this paper, we have solved the Schrödinger wave equation with Yukawa plus ring-shaped potential model using powerful Nikiforov-Uvarov method and obtained the energy eigenvalues and corresponding wave functions in terms of Jacobi and Laguerre polynomials for the angular and radial part respectively. We have also presented the effect of angle dependent solution on radial solutions and also applied our results to obtain numerical values for some selected diatomic molecules which suggest usefulness to other physical systems. We also studied the behavior of our potential graphically for H2 diatomic molecule.

Published in Applied and Computational Mathematics (Volume 6, Issue 1)
DOI 10.11648/j.acm.20170601.14
Page(s) 54-59
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), 2017. Published by Science Publishing Group

Keywords

Noncentral Potential, Diatomic Molecules, Nikiforov-Uvarov Method, Yukawa Potential, Ring-Shaped Potential

References
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[9] Hamzavi, M. and IKhdair, S. M. (2013) Relativistic symmetries of fermions in the background of inverse quadratic Yukawa potential as a tensor. Canadian Journal of Physics. A36, 11807-11818.
[10] Ita, B; Ikot, A; Ikeuba, A. and Ebiekpe, V. (2014) Exact solution of Schrödinger equation for the Inverse quadratic Yukawa potential using Nikiforov-Uvarov method. Journal of Theoretical Physics and Cryptography. Vol. 5, pp.7-11.
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[13] Antia, A. D; Umo, E. A. and Umoren, C. C. (2015) solution of nonrelativistic Schrödinger equation with Hulthen-Yukawa plus ange dependent potential within the framework of Nikiforov-Uvarov method. Journal of Theoretical Physics and Cryptography. Vol. 10, pp.1-8.
[14] Yasuk, F; Durmus, A. and Boztosun, I. (2006) Exact analytical solution to the relativistic Klien-Gordon equation with a noncentral equal scalar and vector potentials. Journal of Mathematics and Physics. 49, 082302.
[15] Hamzavi, M. and Rajabi, A. A. (2011) Exact solution of Dirac equation with Coulomb plus a novel angle dependent potential. Z. Naturforsch. 66a, 533.
[16] Rajabi, A. A. and Hamzavi, M. (2013) A new coulomb ring shaped potential via generalized parametric Nikiforov-Uvarov method. Journal of Theoretical and Applied Physics. 7:17.
[17] Zhang, M. C and Huang-Fu, G. Q. (2011) Pseudospin symmetry for a new oscillatory ring-shaped noncentral potential. Journal of Mathematics and Physics. 52, 053518.
[18] Nikiforov, A. F. and Uvarov, V. B. (1988) Special Functions of Mathematical Physics. Basel: Birkhauser.
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[20] Antia, A. D. and Ikot, A. N. (2014) Relativistic treatment of Spinless particles Subject to the Hulthen plus Yukawa potential with arbituary l-state. Advances in Physics Theory and Applications. Vol. 35, pp.27-35.
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Cite This Article
  • APA Style

    Akaninyene D. Antia, Okon P. Akpan. (2017). Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model. Applied and Computational Mathematics, 6(1), 54-59. https://doi.org/10.11648/j.acm.20170601.14

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    ACS Style

    Akaninyene D. Antia; Okon P. Akpan. Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model. Appl. Comput. Math. 2017, 6(1), 54-59. doi: 10.11648/j.acm.20170601.14

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    AMA Style

    Akaninyene D. Antia, Okon P. Akpan. Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model. Appl Comput Math. 2017;6(1):54-59. doi: 10.11648/j.acm.20170601.14

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  • @article{10.11648/j.acm.20170601.14,
      author = {Akaninyene D. Antia and Okon P. Akpan},
      title = {Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model},
      journal = {Applied and Computational Mathematics},
      volume = {6},
      number = {1},
      pages = {54-59},
      doi = {10.11648/j.acm.20170601.14},
      url = {https://doi.org/10.11648/j.acm.20170601.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170601.14},
      abstract = {In this paper, we have solved the Schrödinger wave equation with Yukawa plus ring-shaped potential model using powerful Nikiforov-Uvarov method and obtained the energy eigenvalues and corresponding wave functions in terms of Jacobi and Laguerre polynomials for the angular and radial part respectively. We have also presented the effect of angle dependent solution on radial solutions and also applied our results to obtain numerical values for some selected diatomic molecules which suggest usefulness to other physical systems. We also studied the behavior of our potential graphically for H2 diatomic molecule.},
     year = {2017}
    }
    

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    T1  - Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model
    AU  - Akaninyene D. Antia
    AU  - Okon P. Akpan
    Y1  - 2017/02/24
    PY  - 2017
    N1  - https://doi.org/10.11648/j.acm.20170601.14
    DO  - 10.11648/j.acm.20170601.14
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
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    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20170601.14
    AB  - In this paper, we have solved the Schrödinger wave equation with Yukawa plus ring-shaped potential model using powerful Nikiforov-Uvarov method and obtained the energy eigenvalues and corresponding wave functions in terms of Jacobi and Laguerre polynomials for the angular and radial part respectively. We have also presented the effect of angle dependent solution on radial solutions and also applied our results to obtain numerical values for some selected diatomic molecules which suggest usefulness to other physical systems. We also studied the behavior of our potential graphically for H2 diatomic molecule.
    VL  - 6
    IS  - 1
    ER  - 

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Author Information
  • Department of Physics, Faculty of Science, University of Uyo, Uyo, Nigeria

  • Department of Science Technology, Akwa Ibom State Polytechnic, Ikot Ekpene, Nigeria

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