Advertisement

Arabian Journal for Science and Engineering

, Volume 39, Issue 1, pp 467–474 | Cite as

Solutions of Dirac Equation with Generalized Rotating Deng-Fan Potential

  • Akpan N. IkotEmail author
  • Oladunjoye A. Awoga
Research Article - Physics

Abstract

We present the approximate solution of the Dirac equation with generalized Rotating Deng-Fan potential under spin and pseudospin symmetry limits using a parametric generalized NIkiforov–Uvarov method to obtain the energy eigenvalue and the corresponding eigen functions in closed form. We also discussed the special cases of this potential which is consistent with those found in other literatures.

Keywords

Dirac equation Nikiforov–Uvarov method Generalized Rotating Deng-Fan potential 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alhaidari, A.D.: Exact solutions of Dirac and Schrodinger equations for a large class of power-law potentials at zero energy. Int. J. Mod. Phys. A. 30, 4551 (2002)Google Scholar
  2. 2.
    Wei, G.F; Dong, S.H.: Approximately analytical solutions of the Manning-Rosen potential with spin–orbit coupling term and spin symmetry. Phys. Lett. A 373, 49 (2008)Google Scholar
  3. 3.
    Ginocchio, J.N.: Relativistic symmetries in nuclei and hadrons. Phys. Rep. 414, 165 (2005)Google Scholar
  4. 4.
    Troltenier, D.; Bahri, C.; Draayar, J.P.: Generalized pseudo SU(3) model and pairing. Nucl. Phys. A 586, 53 1995Google Scholar
  5. 5.
    Page, P.R.; Goldman, T.; Ginocchio, J.N.: Relativistic symmetry suppresses quark spin orbit splitting. Phys. Rev. Lett. 86, 204 (2001)Google Scholar
  6. 6.
    Ginocchio J.N.: Pseudospin as a relativistic symmetry. Phys. Rev. Lett. 78(3), 436 (1997)CrossRefGoogle Scholar
  7. 7.
    Ginocchio, J.N.; Leviatan, A.; Meng, J.; Zhou, S.G.: Test of pseudospin symmetry in deformed nuclei. Phys. Rev. C 69, 034303 (2004)Google Scholar
  8. 8.
    Hamzari, M.; Rajabi, A.A.; Hassanabadi, H.: Relativistic Morse potential and tensor interaction. Few-Body Syst. 52, 19 (2012)Google Scholar
  9. 9.
    Berkdemir, C.; Berkdemir, A.; Sever, R.: J. Phys. A: Math. Gen. 39, 13455 (2006)Google Scholar
  10. 10.
    Egrifes, H.; Sever, R.: Bound state solutions of the Klein-Gordon equation for the generalized PT-symmetric Hulthen potential. Int. J. Theor. Phys. 46, 935 (2008)Google Scholar
  11. 11.
    Arda, A.; Sever, R.; Tezcan, C.; Akcay, H.: Effective mass Dirac-morse Problem with any κ-value. Chin. Phys. Lett. 27, 040306 (2010)Google Scholar
  12. 12.
    Hamzavi, M.; Rajabi, A.A.; Hassanabadi, H.: Exact spin and pseudospin symmetry solutions of the Dirac equation with pseudoharmonic potential including linear plus Coulomb-like tensor. Int. J. Mod. Phys. A. 26(7 & 8), 1363 (2011)Google Scholar
  13. 13.
    Hamzavi, M.; Hassanabadi, H.; Rajabi, A.A.: Exact solution of the Dirac equation equation for the Mie-type potential by using the Nikiforov-uvarov method under the pseudospin and spin symmetry limit. Mod. Phys. Lett. A 25(28), 2447 (2010)Google Scholar
  14. 14.
    Ikhdair, S.M.; Sever, R.: Approximate bound state solutions of Dirac equations with Hulthen potential including Coulomb-like tensor potential. Appl. Math. Comput. 216, 911 (2010)Google Scholar
  15. 15.
    Ikot, A.N.: Solutions of Dirac equation for generalized hyperbolical potential including Coulomb-like potential with spin symmetry. Few-Body Syst. 53, 549. doi: 10.1007/s 00601-012-0451-x. (2012)
  16. 16.
    Ikot, A.N., Akpabio, L.E.; Uwah, E.J.: Bound state solutions of the Klein-Gordon equation with the Hulthen potential. Electron. J. Theor. Phys. 8, 225Google Scholar
  17. 17.
    Ikot, A.N.: Awoga, O.A; Ita, B.I.: Exact solution of the Klein-Gordon equation with Hylleraas potential. Few-Body Syst. 2012,53,539. doi: 10-1007/s00601-012-0434-y
  18. 18.
    Ikot, A.N.: Solutions of the Klein–Gordon equation with equal scalar and vector modigied Hylleraas plus exponential Rosen–Morse potential. Chin. Phys. Lett. 29(6), 060307 (2012)Google Scholar
  19. 19.
    Dong S.H.: Relativistic treatment of spinless particles subject to a rotating Deng-Fan oscillator. Commun. Theor. Phys. 55, 969 (2011)CrossRefzbMATHGoogle Scholar
  20. 20.
    Ikhdair, S.M.: An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry. J. Math. Phys. 52, 052303 (2011)Google Scholar
  21. 21.
    Goldman, I.I.; Krivchenkov: Problems in Quantum Mechanics. Pergamm, New York (1961)Google Scholar
  22. 22.
    Deng, Z.H.; Fan, Y.P.: Shandong Univ. J. 7, 162 (1957)Google Scholar
  23. 23.
    Mesa, A.D.S; Quesne, C.; Smirnov, Y.F.: Generalized Morse potential :symmetry and satellite potentials. J. Phys. A Math. Gen. 31, 321 (1998)Google Scholar
  24. 24.
    Nikiforov, A.F.: Uvarov, V.B.: Special Functions of Mathematical Physics. Birkhauser, Basel (1988)Google Scholar
  25. 25.
    Tezcan, C.; Sever, R.: A general approach for the exact solution of the Schrodinger equation Int. J. Theor. Phys. 48, 337 (2009)Google Scholar
  26. 26.
    Hamzavi, M.; Rajabi, A.A.; Hassanabadi, H.: Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like interaction via asymptotic iteration method. Phys. Lett. A 374, 4303 (2010)Google Scholar
  27. 27.
    Greene, R.L.; Aldrich, C.: Variational wave functions for a screened Coulomb potential Phys. Rev. A 14, 2363 (1976)Google Scholar
  28. 28.
    Qiang, W.C; Dong, S.H.: Analytical Approximation to the solutions of the Manning-Rosen potential with centrifugal term. Phys. Lett. A 368, 13 (2007)Google Scholar
  29. 29.
    Dong, S.H.; Qiang, W.C.; Sun, G.H.; Bezarra, V.B.: Analytical approximation to the l-wave solutions of the Schrodinger equation with the Eckart potential. J. Phys. A 40, 10535 (2007)Google Scholar
  30. 30.
    Dong, S.H.; Qiang, W.C.: Analytical approximations to the Schrodinger equation for the second Poschl-Teller like potential with centrifugal term. Int. J. Mod. Phys. A 23, 1537 (2008)Google Scholar
  31. 31.
    Qiang, W.C.; Dong, S.H.: Analytical approximation to the l-wave solutions of the Klein–Gordon equation for a second Poschl-Teller like potential. Phys. Lett. A 372, 4789 (2008)Google Scholar
  32. 32.
    Wei, G.F.; Zhen, Z.Z.; Dong, S.H.: The relativistic bound state scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term. Central Eur. J. Phys. 7(1), 175 (2009)Google Scholar
  33. 33.
    Wei, G.F.; Dong, S.H.; Bezerra, V.: The relativistic bound and scattering states of the Eckart potential with properly new approximate scheme to the centrifugal term. Int. J. Modern Phys. A 24(1), 161 (2009)Google Scholar
  34. 34.
    Qiang, W.C.; Dong, S.H.: The Manning-Rosen potential studied by a new approximate scheme to the centrifugal term. Phys. Scr. 79, 045004 (2009)Google Scholar
  35. 35.
    Meng, J.; Sugawara-Tanabe, K.; Yamaji, S.; Ring, P.; Arima, A.: Phys. Rev. C. 50, 154 (1999)Google Scholar
  36. 36.
    Wei, G.F.: Dong, S.H.: Algebraic approach to pseudospin symmetry for Dirac equation with scaler and vector modified Poschl–Teller potential. Euro. Phys. Lett. 87, 4004 (2009)Google Scholar
  37. 37.
    Wei, G.F., Dong, S.H.: The spin symmetry for deformed generalized Poschl–Teller potential, Phys. Lett. A 373, 2428 (2009)Google Scholar
  38. 38.
    Wei, G.F.; Dong, S.H.: Spin symmetry in the relativistic symmetrical well potential including a proper approximation to the spin-orbit coupling term. Phys. Scr. 81, 035009 (2010)Google Scholar
  39. 39.
    Wei, G.F.; Dong, S.H.: Pseudospin symmetry in the relativistic Manning-Rosen potential including a Pekeris approximation to the pseudo-centrifugal term. Phys. Lett. B 689, 288 (2010)Google Scholar

Copyright information

© King Fahd University of Petroleum and Minerals 2013

Authors and Affiliations

  1. 1.Theoretical Physics Group, Department of PhysicsUniversity of UyoUyoNigeria

Personalised recommendations