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Bound states of spatially dependent mass Dirac equation with the Eckart potential including Coulomb tensor interaction

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Abstract

We investigate the approximate solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential field including the Coulomb tensor interaction by using the parametric Nikiforov-Uvarov method. Taking an appropriate approximation to deal with the centrifugal term, the Dirac energy states and the corresponding normalized two-spinor components of the wave function are obtained in closed form. Some special cases of our solution are investigated. Furthermore, we present the correct solutions obtained via the asymptotic iteration method which are in agreement with the parametric Nikiforov-Uvarov method results.

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References

  1. S.M. Ikhdair, R. Sever, Phys. Scr. 79, 035002 (2009).

    Article  ADS  Google Scholar 

  2. S.M. Ikhdair, Eur. Phys. J. A 40, 143 (2009).

    Article  ADS  Google Scholar 

  3. M. Eshghi, M. Hamzavi, S.M. Ikhdair, Adv. High Energy Phys. 2012, 873619 (2012).

    Article  MathSciNet  Google Scholar 

  4. M. Eshghi, M. Hamzavi, S.M. Ikhdair, Chin. Phys. B 22, 030303 (2013).

    Article  ADS  Google Scholar 

  5. I.C. Wang, C.Y. Wong, Phys. Rev. D 38, 348 (1988).

    Article  ADS  Google Scholar 

  6. G. Mao, Phys. Rev. C 67, 044318 (2003).

    Article  ADS  Google Scholar 

  7. R.J. Furnstahl, J.J. Rusnak, B.D. Serot, Nucl. Phys. A 632, 607 (1998).

    Article  ADS  Google Scholar 

  8. P. Alberto, R. Lisboa, M. Malheiro, A.S. de Castro, Phys. Rev. C 71, 034313 (2005).

    Article  ADS  Google Scholar 

  9. Y.I. Salamin, S. Hu, K.Z. Hatsagortsyan, C.H. Keitel, Phys. Rep. 427, 41 (2006).

    Article  ADS  Google Scholar 

  10. M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nature Phys. 2, 620 (2006).

    Article  ADS  Google Scholar 

  11. M.R. Galler, W. Kohn, Phys. Rev. Lett. 70, 3103 (1993).

    Article  ADS  Google Scholar 

  12. A. Puente, M. Gasas, Comput. Mater. Sci. 2, 441 (1994).

    Article  Google Scholar 

  13. F.A. De Saavedra, J. Boronat, A. Polls, A. Fabrocini, Phys. Rev. B 50, 4248 (1994).

    Article  ADS  Google Scholar 

  14. M. Barranco, M. Pi, S.M. Gatica, E.S. Hernandez, J. Navarro, Phys. Rev. B 56, 8997 (1997).

    Article  ADS  Google Scholar 

  15. A. Puente, L.I. Serra, M. Casas, Z. Phys. D 31, 283 (1994).

    Article  ADS  Google Scholar 

  16. L.I. Serra, E. Lipparini, Europhys. Lett. 40, 667 (1997).

    Article  ADS  Google Scholar 

  17. G. Bastard Wave Mechanics Applied to Semiconductor Heterostructures (Les Editions de physique, Les Ulis, 1988).

  18. A.G.M. Schmidt, Phys. Lett. A 353, 459 (2006).

    Article  ADS  Google Scholar 

  19. S.M. Ikhdair, R. Sever, Appl. Math. Comput. 216, 545 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  20. M. Hamzavi, M. Eshghi, S.M. Ikhdair, J. Math. Phys. 53, 082101 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  21. M.C. Zhang, G.Q. Huang-Fu, Ann. Phys. 327, 841 (2012).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  22. M. Eshghi, M. Hamzavi, Commun. Theor. Phys. 57, 355 (2012).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  23. M. Eshghi, H. Mehraban, Few-Body Syst. 52, 207 (2012).

    Article  Google Scholar 

  24. M. Hamzavi, A.A. Rajabi, H. Hassanabadi, Phys. Lett. A 374, 4303 (2010).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  25. M. Hamzavi, A. Rajabi, Commun. Theor. Phys. 55, 35 (2011).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  26. M. Hamzavi, A. Rajabi, Ann. Phys. (NY) 334, 316 (2013).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  27. A.A. Rajabi, H. Hamzavi, Eur. Phys. J. Plus 128, 5 (2013) DOI:10.1140/epjp/i2013-13005-5.

    Article  Google Scholar 

  28. S.M. Ikhdair, Few-Body Syst. 54, 1987 (2013) DOI:10.1007/s00601-013-0693-2.

    Article  ADS  Google Scholar 

  29. M. Hamzavi, H. Hassanabadi, A.A. Rajabi, Int. J. Theor. Phys. 50, 454 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  30. A.F. Nikiforov, V.B. Uvarov, Special Functions of Mathematical Physics (Birkhauser, Berlin, 1988).

  31. S.M. Ikhdair, Int. J. Mod. Phys. C 20, 1563 (2009).

    Article  ADS  MATH  Google Scholar 

  32. S.M. Ikhdair, Eur. Phys. J. A 39, 307 (2009).

    Article  ADS  Google Scholar 

  33. S.M. Ikhdair, J. Math. Phys. 52, 052303 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  34. S.M. Ikhdair, R. Sever, J. Math. Phys. 52, 122108 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  35. S.M. Ikhdair, J. Math. Phys. 51, 023525 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  36. S.M. Ikhdair, C. Berkdemir, R. Sever, Appl. Math. Comput. 217, 9019 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  37. M. Hamzavi, S.M. Ikhdair, M. Solaimani, Int. J. Mod. Phys. E 21, 1250016 (2012).

    Article  ADS  Google Scholar 

  38. M. Hamzavi, S.M. Ikhdair, K.E. Thylwe, Int. J. Mod. Phys. E 21, 1250097 (2012).

    Article  ADS  Google Scholar 

  39. Y.A. Yahya, B.J. Falaye, O.J. Oluwadare, K.J. Oyewumi, Int. J. Mod. Phys. E 22, 1350062 (2010).

    Article  Google Scholar 

  40. S.M. Ikhdair, M. Hamzavi, B.J. Falaye, Appl. Math. Comput. 225, 775 (2013).

    Article  MathSciNet  Google Scholar 

  41. S.M. Ikhdair, Cent. Eur. J. Phys. 10, 361 (2012).

    Article  Google Scholar 

  42. M. Hamzavi, S.M. Ikhdair, K.E. Thylwe, Z. Naturforsch. 67a, 567 (2012).

    Article  Google Scholar 

  43. S.M. Ikhdair, B.J. Falaye, Phys. Scr. 87, 035002 (2013).

    Article  ADS  Google Scholar 

  44. S.M. Ikhdair, B.J. Falaye, M. Hamzavi, Chin. Phys. Lett. 30, 020305 (2013).

    Article  Google Scholar 

  45. Zhang Ai-Ping, Qiang Wen-Chao, Ling Ya-Wen, Chin. Phys. Lett. 26, 100302 (2009).

    Article  ADS  Google Scholar 

  46. Qiang Wen-Chao, Wu Jing-Yang, Dong Shi-Hai, Phys. Scr. 79, 065011 (2009).

    Article  ADS  Google Scholar 

  47. Wei Gao-Feng, Long Chao-Yun, Duan Xiao-Yong, Dong Shi-Hai, Phys. Scr. 77, 035001 (2008).

    Article  ADS  Google Scholar 

  48. Chen Chang-Yuan, Sun Dong-Sheng, Lu Fa-Lin, J. Phys. A: Math. Theor. 41, 035302 (2008).

    Article  ADS  Google Scholar 

  49. Zhang Min-Cang, Huang-Fu Guo-Qing, Phys. Scr. 85, 015005 (2012).

    Article  ADS  Google Scholar 

  50. C. Eckart, Phys. Rev. 35, 1303 (1930).

    Article  ADS  MATH  Google Scholar 

  51. B.J. Falaye, Cent. Eur. J. Phys. 10, 960 (2012).

    Article  Google Scholar 

  52. Y. Chen et al., Acta Chim. Sin. 50, 1163 (1992) (in Chinese).

    Google Scholar 

  53. F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  54. J.J. Weiss, J. Chem. Phys. 41, 1120 (1964).

    Article  ADS  Google Scholar 

  55. A. Cimas, M. Aschi, C. Barrientos, V.M. Rayón, J.A. Sordo, A. Largo, Chem. Phys. Lett. 374, 594 (2003).

    Article  ADS  Google Scholar 

  56. W. Greiner, Relativistic Quantum Mechanics (Springer, Berlin, 2000) p. 231.

  57. R.L. Greene, C. Aldrich, Phys. Rev. A 14, 2363 (1976).

    Article  ADS  Google Scholar 

  58. M. Hamzavi, S.M. Ikhdair, B.I. Ita, Phys. Scr. 85, 045009 (2012).

    Article  ADS  Google Scholar 

  59. S.M. Ikhdair, R. Sever, Appl. Math. Comput. 216, 911 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  60. Zou Xia, Yi Liang-Zhong, Jia Chun-Sheng, Phys. Lett. A 346, 54 (2005).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  61. S.M. Ikhdair, J. Quantum Inf. Sci. 1, 73 (2011).

    Article  Google Scholar 

  62. L.Z. Yi, Y.F. Diao, J.Y. Liu, C.S. Jia, Phys. Lett. A 333, 212 (2004).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  63. L. Hulthén, Ark. Mat. Astron. Fys. 28, 5 (1942).

    Google Scholar 

  64. G. Malli, Chem. Phys. Lett. 26, 578 (1981).

    Article  ADS  Google Scholar 

  65. C.S. Lai, Phys. Lett. A 112, 211 (1985).

    Article  ADS  Google Scholar 

  66. J.D. Dow, Phys. Rev. Lett. 30, 903 (1973).

    Article  ADS  Google Scholar 

  67. J.A. Olson, D.A. Micha, J. Chem. Phys. 68, 4352 (1978).

    Article  ADS  Google Scholar 

  68. A. Del Sol Mesa, C. Quesne, Y.F. Smirnov, J. Phys.: Math. Gen. 31, 321 (1998).

    ADS  MATH  Google Scholar 

  69. S. Codriansky, P. Cordero, S. Salamó, J. Phys. A: Math. Gen. 32, 6287 (1999).

    Article  ADS  MATH  Google Scholar 

  70. M.K. Bahar, F. Yasuk, Chin. Phys. B 22, 010301 (2013).

    Article  ADS  Google Scholar 

  71. N. Saad, Phys. Scr. 76, 623 (2007).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  72. G.B. Arfken, H.J. Weber, Mathematical Methods for Physicists (Academic Press, San Diego, 1995).

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Authors and Affiliations

  1. Department of Physics, Faculty of Science, An-Najah National University, New Campus, Nablus, West Bank, Palestine

    Sameer M. Ikhdair

  2. Department of Physics, Near East University, 922022, Nicosia, Northern Cyprus

    Sameer M. Ikhdair

  3. Theoretical Physics Section, University of Ilorin, Ilorin, Nigeria

    Babatunde J. Falaye

  4. Mersin 10, Turkey

    Sameer M. Ikhdair

Authors
  1. Sameer M. Ikhdair
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  2. Babatunde J. Falaye
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Correspondence to Babatunde J. Falaye.

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Ikhdair, S.M., Falaye, B.J. Bound states of spatially dependent mass Dirac equation with the Eckart potential including Coulomb tensor interaction. Eur. Phys. J. Plus 129, 1 (2014). https://doi.org/10.1140/epjp/i2014-14001-y

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