American Journal of Physical Chemistry

| Peer-Reviewed |

Solutions of Nonrelativistic Schrödinger Equation with Scarf II Plus Rosen-Morse II Potential via Ansaltz Method

Received: 25 August 2015    Accepted: 06 September 2015    Published: 20 October 2015
Views:       Downloads:

Share This Article

Abstract

We have solved the non-relativistic Schrödinger equation with Scarf II plus Rosen-Morse II potential analytically for arbitrary l-state by using the newly improved ansaltz for the wave function and adopting the modified approximation scheme to evaluate the centrifugal term. The bound state energy spectrum and the un-normalized wave function expressed in terms of Jacobi polynomial are also obtained. With this method, we have obtained a negative energy spectrum for the system.

DOI 10.11648/j.ajpc.20150405.11
Published in American Journal of Physical Chemistry (Volume 4, Issue 5, October 2015)
Page(s) 38-41
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

Non-Relativistic Schrödinger Equation, Scarf II Potential, Rosen-Morse II Potential, Bound State, Wave Function

References
[1] L. Z. Yi, Y. F. Diao, J. Y. Liu, C. S. Jia. Bound state of the Klein-Gordon equation with vector and scalar Rosen-Morse type potentials. Physics Letter A, Vol. 333, 212, 2004.
[2] A. N. Ikot. Analytical solutions of Schrodinger equation with generalized hyperbolic potential using Nikiforov-Uvarov method. African Review of Physics, Vol. 6, No. 0026, pp. 221-228, 2011.
[3] A. D. Antia, I. E. Essien, E. B. Umoren, C. C. Eze. Approximate solutions of the non-relativistic Schrodinger equation with inversely quadratic Yukawa plus Mobius square potential via parametric Nikiforov-Uvarov method. Advances in Physics Theories and Applications, Vol. 44, pp.1-13, 2015.
[4] A. D. Antia, I. O. Akpan, A. O. Akankpo.Relativistic treatment of spinless particles subject to modified Scarf II potential. International Journal of High Energy Physics, Vol. 2, No.4, pp.50-55, 2015.
[5] A. D. Antia, A. N. Ikot, E. E. Ituen, I. O. Akpan. Bound state solutions of the Klein-Gordon equation for deformed Hulthen potential with position dependent mass. Sri Lankan Journal of Physics, Vol. 13, No. 1, pp. 27-40, 2012.
[6] H. Hassanabadi, S. Zarrinkamar and A. A. Rajabi. Exact solutions of D-dimensional Schrodinger equation for energy-dependent potential by Nikiforov-Uvarov method. Communications in Theoretical Physics, Vol. 55, 541, 2011.
[7] W. C. Qiang and S. H. Dong. The Manning-Rosen potential studied by a new approximation scheme to the centrifugal term. Physica Scripta, Vol. 79, 045004, 2009.
[8] A. D. Antia, A. N. Ikot, H. Hassanabadi and E. Maghsoodi. Bound state solutions of Klein-Gordon equation with Mobius square plus Yukawa potentials. Indian Journal of Physics, Vol. 87, No. 11, pp.1133-1139, 2013.
[9] G. F. Wei, C. Y. Long and S. H. Dong. The scattering of the Manning-Rosen potential with centrifugal term. Physica Scripta, Vol. 77, 035001, 2008.
[10] S. Dong, S. H. Garcia-Ravalo and S. H. Dong. Quantization rule solution to the Hulthen potential in arbitrary l-state. Physica Scripta, Vol. 76, 393, 2007.
[11] J. Lu. Approximate spin and pseudospin solutions of the Dirac equation. Physica Scripta, Vol. 72, 349, 2005.
[12] R. L. Greene and C. Aldrich. Variational wave functions for a screened coulomb potential. Physical Revision A, Vol. 14, 2363, 1976.
[13] C. S. Jia, T. Chen and L. G. Cui. Approximate analytical solutions of the Dirac equation with the generalized Poschl-Teller potential including the pseudo-spin centrifugal term. Physics Letter A, Vol. 373, pp.1621-1626, 2009.
[14] E. H. Hill. The theory of vector spherical harmonics. American Journal of Physics, Vol. 22, pp.211-221, 1954.
[15] F. Yasuk and M. K. Bahar. Approximate solutions of the Dirac equation with position-dependent mass for the Hulthen potential by the asymptotic iteration method. Physica Scripta, Vol. 85, 045004, 2012.
[16] H. Hassanabadi, E. Maghsoodi and S. Zarrinkamar. Relativistic symmetries of Dirac equation and the Tietz potential. European Physics Journal Plus, Vol. 127, 31, 2012.
[17] M. Bag, M. M. Panja, R. Dutt and Y. P. Varshni. Modified shifted large-N approach to the Morse potential. Physical Review A, Vol. 46, pp. 6059-6065, 1992.
[18] A. D. Antia, E. E. Ituen, H. P. Obong and C. N. Isonguyo. Analytical solutions of the modified coulomb potential using the factorization method. International Journal Recent advances in Physics, Vol. 4, No. 1, pp.55-65, 2015.
[19] S. M. Ikhdair and R. Sever. Exact polynomial eigen solution of Schrodinger for pseudo harmonics potential. International Journal of Modern Physics, Vol.19, pp.221-229, 2008.
[20] A. F. Nikiforov and V. B. Uvarov. Special Functions of mathematical Physics (Basel: Birkhauser), 1988.
[21] A. N. Ikot. Solutions of the Klein-Gordon equation with equal scalar and vector modified Hylleraas plus exponential Rosen-Morse potential. Chinese Physics Letter, Vol. 29, 060307, 2012.
[22] H. Hassanabadi, B. H. Yazarlo, S. Zarrinkamar and A. A. Rajabi. Duff-Kemmer-Petiau equation under a scalar Coulomb interaction. Physics Revision C, Vol. 84, 064003, 2011.
[23] A. N. Ikot, L. E. Akpabio and E. B. Umoren. Exact solution of Schrodinger equation with inverted Woods-Saxon and Manning-Rosen potential. Journal of Scientific Research, Vol. 3, No. 1, pp. 25-33, 2011.
[24] L. D. Landau and E. M. Lifshitz. Quantum Mechanics, Non-relativistic Theory (Canada: Pergamon), 1977.
[25] L. I. Schiff. Quantum Mechanics (New York: McGraw Hill), 1955.
[26] A. D. Polyanin and A. V. Manzhirov. Handbook of integrals equation (CRC press Boca Rotan), doi: 10.1201/9781420050066, 1998.
[27] M. R. Pahlavai, J. Sadeghi and M. Ghezelbash. Applied Science, Vol. 11, 106, 2009.
[28] K. M. Khanna, G. F. Kanyeki, S. K. Rotich, P. K. Torongey and S. E. Ameka. Indian Journal Pure and Applied Physics, Vol. 48, 7, 2010.
Author Information
  • Theoretical Physics Group, Department of Physics, Faculty of Science, University of Uyo, Uyo, Akwa Ibom State, Nigeria

Cite This Article
  • APA Style

    Akaninyene D. Antia. (2015). Solutions of Nonrelativistic Schrödinger Equation with Scarf II Plus Rosen-Morse II Potential via Ansaltz Method. American Journal of Physical Chemistry, 4(5), 38-41. https://doi.org/10.11648/j.ajpc.20150405.11

    Copy | Download

    ACS Style

    Akaninyene D. Antia. Solutions of Nonrelativistic Schrödinger Equation with Scarf II Plus Rosen-Morse II Potential via Ansaltz Method. Am. J. Phys. Chem. 2015, 4(5), 38-41. doi: 10.11648/j.ajpc.20150405.11

    Copy | Download

    AMA Style

    Akaninyene D. Antia. Solutions of Nonrelativistic Schrödinger Equation with Scarf II Plus Rosen-Morse II Potential via Ansaltz Method. Am J Phys Chem. 2015;4(5):38-41. doi: 10.11648/j.ajpc.20150405.11

    Copy | Download

  • @article{10.11648/j.ajpc.20150405.11,
      author = {Akaninyene D. Antia},
      title = {Solutions of Nonrelativistic Schrödinger Equation with Scarf II Plus Rosen-Morse II Potential via Ansaltz Method},
      journal = {American Journal of Physical Chemistry},
      volume = {4},
      number = {5},
      pages = {38-41},
      doi = {10.11648/j.ajpc.20150405.11},
      url = {https://doi.org/10.11648/j.ajpc.20150405.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajpc.20150405.11},
      abstract = {We have solved the non-relativistic Schrödinger equation with Scarf II plus Rosen-Morse II potential analytically for arbitrary l-state by using the newly improved ansaltz for the wave function and adopting the modified approximation scheme to evaluate the centrifugal term. The bound state energy spectrum and the un-normalized wave function expressed in terms of Jacobi polynomial are also obtained. With this method, we have obtained a negative energy spectrum for the system.},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Solutions of Nonrelativistic Schrödinger Equation with Scarf II Plus Rosen-Morse II Potential via Ansaltz Method
    AU  - Akaninyene D. Antia
    Y1  - 2015/10/20
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ajpc.20150405.11
    DO  - 10.11648/j.ajpc.20150405.11
    T2  - American Journal of Physical Chemistry
    JF  - American Journal of Physical Chemistry
    JO  - American Journal of Physical Chemistry
    SP  - 38
    EP  - 41
    PB  - Science Publishing Group
    SN  - 2327-2449
    UR  - https://doi.org/10.11648/j.ajpc.20150405.11
    AB  - We have solved the non-relativistic Schrödinger equation with Scarf II plus Rosen-Morse II potential analytically for arbitrary l-state by using the newly improved ansaltz for the wave function and adopting the modified approximation scheme to evaluate the centrifugal term. The bound state energy spectrum and the un-normalized wave function expressed in terms of Jacobi polynomial are also obtained. With this method, we have obtained a negative energy spectrum for the system.
    VL  - 4
    IS  - 5
    ER  - 

    Copy | Download

  • Sections