International Journal of Applied Mathematics and Theoretical Physics

| Peer-Reviewed |

Heavy Quarkonia and  Mesons in the Cornell Potential with Harmonic Oscillator Potential in the N-dimensional Schrödinger Equation

Received: 15 July 2016    Accepted: 27 July 2016    Published: 30 August 2016
Views:       Downloads:

Share This Article

Abstract

Heavy quarkonia,  meson, and  -meson masses are calculated within the framework of the N-dimensional radial Schrödinger equation. The Cornell potential is extended by including the harmonic oscillator potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov-Uvarov (NV) method. The energy eigenvalues are obtained in the three-dimensional space. The mass of spectra of charmonium, bottomonium, , and  mesons are calculated. The effect of dimensionality number on the mass of quarkonium is investigated. A comparison with other theoretical approaches is discussed. The obtained results are in good agreement with experimental data. We conclude that the dimensionality number plays an important role in studying the spectra of quarkonium masses. The modified Cornell potential provides a good description of the spectra of quarkonium masses.

DOI 10.11648/j.ijamtp.20160202.11
Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 2, April 2016)
Page(s) 16-20
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

Heavy Quarkonia, Quarkonium States, Cornell Potential

References
[1] S. M. Kuchin and N. V. Maksimenko, Univ. J. Phys. Appl. 7, 295 (2013).
[2] R. Kumar and F. Chand, Commun. Theor. Phys. 59, 528 (2013).
[3] A. Al-Jamel and H. Widyan, Appl. Phys. Rese. 4, 94 (2013).
[4] H. Ciftci, R. Hall, and N. Saad, J. Phys. A: Math. Gen. 36, 11807 (2003).
[5] Af. Nikiforov Uvarov, "Special Functions of Mathematical Physics" Birkhauser, Basel (1988).
[6] H. S. Chung and J. Lee, J. Kore. Phys. Soci. 52, 1151 (2008).
[7] N. V. Masksimenko and S. M. Kuchin, Russ. Phy. J. 54, 57 (2011).
[8] Z. Ghalenovi, A. A. Rajabi, S. Qin and H. Rischke, hep-ph/14034582 (2014).
[9] S. M. Ikhdair, quant-ph/11100340 (2011).
[10] B. J. Vigo-Aguir and T. E. Simos, Int. J. Quantum Chem. 103, 278 (2005).
[11] P. Gupta and I. Mechrotra, J. Mod. Phys. 3, 1530 (2012).
[12] R. Kumar and F. Chand, Phys. Scr. 85, 055008 (2012).
[13] J. Beringer et al. [particle Data Group], Phys. Rev. D 86, 1 (2012).
[14] A. Kumar Ray and P. C. Vinodkumar, Pramana J. Phys. 66, 958 (2006).
[15] E. J. Eichten and C. Quigg, Phys. Rev. D 49, 5845 (1994).
[16] D. Ebert, R. N. Faustov, and V. O. Galkin, Phys. Rev. D 67, 014027 (2003).
[17] L. I. Abou-Salem, Inter. J. Mod. Phys. A 20, 4113 (2005).
[18] Particle Data Group, Phys. Rev. D 54, 1 (1996).
[19] S. Godfrey and K. Moats, hep-ph/14090874 (2014).
Author Information
  • Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt

Cite This Article
  • APA Style

    M. Abu-Shady. (2016). Heavy Quarkonia and  Mesons in the Cornell Potential with Harmonic Oscillator Potential in the N-dimensional Schrödinger Equation. International Journal of Applied Mathematics and Theoretical Physics, 2(2), 16-20. https://doi.org/10.11648/j.ijamtp.20160202.11

    Copy | Download

    ACS Style

    M. Abu-Shady. Heavy Quarkonia and  Mesons in the Cornell Potential with Harmonic Oscillator Potential in the N-dimensional Schrödinger Equation. Int. J. Appl. Math. Theor. Phys. 2016, 2(2), 16-20. doi: 10.11648/j.ijamtp.20160202.11

    Copy | Download

    AMA Style

    M. Abu-Shady. Heavy Quarkonia and  Mesons in the Cornell Potential with Harmonic Oscillator Potential in the N-dimensional Schrödinger Equation. Int J Appl Math Theor Phys. 2016;2(2):16-20. doi: 10.11648/j.ijamtp.20160202.11

    Copy | Download

  • @article{10.11648/j.ijamtp.20160202.11,
      author = {M. Abu-Shady},
      title = {Heavy Quarkonia and  Mesons in the Cornell Potential with Harmonic Oscillator Potential in the N-dimensional Schrödinger Equation},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {2},
      number = {2},
      pages = {16-20},
      doi = {10.11648/j.ijamtp.20160202.11},
      url = {https://doi.org/10.11648/j.ijamtp.20160202.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijamtp.20160202.11},
      abstract = {Heavy quarkonia,  meson, and  -meson masses are calculated within the framework of the N-dimensional radial Schrödinger equation. The Cornell potential is extended by including the harmonic oscillator potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov-Uvarov (NV) method. The energy eigenvalues are obtained in the three-dimensional space. The mass of spectra of charmonium, bottomonium, , and  mesons are calculated. The effect of dimensionality number on the mass of quarkonium is investigated. A comparison with other theoretical approaches is discussed. The obtained results are in good agreement with experimental data. We conclude that the dimensionality number plays an important role in studying the spectra of quarkonium masses. The modified Cornell potential provides a good description of the spectra of quarkonium masses.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Heavy Quarkonia and  Mesons in the Cornell Potential with Harmonic Oscillator Potential in the N-dimensional Schrödinger Equation
    AU  - M. Abu-Shady
    Y1  - 2016/08/30
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ijamtp.20160202.11
    DO  - 10.11648/j.ijamtp.20160202.11
    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  - 16
    EP  - 20
    PB  - Science Publishing Group
    SN  - 2575-5927
    UR  - https://doi.org/10.11648/j.ijamtp.20160202.11
    AB  - Heavy quarkonia,  meson, and  -meson masses are calculated within the framework of the N-dimensional radial Schrödinger equation. The Cornell potential is extended by including the harmonic oscillator potential. The energy eigenvalues and the corresponding wave functions are calculated in the N-dimensional space using the Nikiforov-Uvarov (NV) method. The energy eigenvalues are obtained in the three-dimensional space. The mass of spectra of charmonium, bottomonium, , and  mesons are calculated. The effect of dimensionality number on the mass of quarkonium is investigated. A comparison with other theoretical approaches is discussed. The obtained results are in good agreement with experimental data. We conclude that the dimensionality number plays an important role in studying the spectra of quarkonium masses. The modified Cornell potential provides a good description of the spectra of quarkonium masses.
    VL  - 2
    IS  - 2
    ER  - 

    Copy | Download

  • Sections