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

Akaninyene D. Antia; Okon P. Akpan

doi:doi:10.11648/j.acm.20170601.14

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

Akaninyene D. Antia, Okon P. Akpan

Published in Applied and Computational Mathematics (Volume 6, Issue 1)

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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[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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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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TY  - JOUR
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
JO  - Applied and Computational Mathematics
SP  - 54
EP  - 59
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

Akaninyene D. Antia

Department of Physics, Faculty of Science, University of Uyo, Uyo, Nigeria
Okon P. Akpan

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
JO  - Applied and Computational Mathematics
SP  - 54
EP  - 59
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  -

Copy | Download