About this Journal Submit a Manuscript Table of Contents
Advances in High Energy Physics
Volume 2013 (2013), Article ID 491648, 10 pages
http://dx.doi.org/10.1155/2013/491648
Research Article

Relativistic Bound States of Spinless Particle by the Cornell Potential Model in External Fields

1Department of Physics, Faculty of Science, An-Najah National University, Nablus, West Bank, Palestine
2Department of Electrical and Electronic Engineering, Near East University, 922022 Nicosia, Northern Cyprus, Turkey

Received 7 May 2013; Accepted 4 August 2013

Academic Editor: Ira Rothstein

Copyright © 2013 Sameer M. Ikhdair. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. W. Thomas and W. Weise, Structure of the Nucleon, Wiley-VCH, Berlin, Germany, 2001.
  2. B. Thaller, The Dirac Equation, Springer, New York, NY, USA, 1992.
  3. T.-Y. Wu and W.-Y. P. Hwang, Relativistic Quantum Mechanics and Quantum Fields, World Scientific, Singapore, 1991. View at Zentralblatt MATH · View at MathSciNet
  4. A. S. de Castro, “Klein-Gordon particles in mixed vector-scalar inversely linear potentials,” Physics Letters A, vol. 338, no. 2, pp. 81–89, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. S. M. Ikhdair, “Exact Klein-Gordon equation with spatially dependent masses for unequal scalar-vector Coulomb-like potentials,” European Physical Journal A, vol. 40, no. 2, pp. 143–149, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. W.-C. Qiang, R.-S. Zhou, and Y. Gao, “Any l-state solutions of the Klein-Gordon equation with the generalized Hulthén potential,” Physics Letters A, vol. 371, no. 3, pp. 201–204, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. S. M. Ikhdair, “Approximate solutions of the dirac equation for the rosen-morse potential including the Spin-orbit centrifugal term,” Journal of Mathematical Physics, vol. 51, no. 2, Article ID 023525, 16 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. S. M. Ikhdair, “An approximate κ state solutions of the Dirac equation for the generalized Morse potential under spin and pseudospin symmetry,” Journal of Mathematical Physics, vol. 52, no. 5, Article ID 052303, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. F. Cooper, A. Khare, and U. Sukhatme, “Supersymmetry and quantum mechanics,” Physics Report, vol. 251, no. 5-6, pp. 267–385, 1995. View at MathSciNet · View at Scopus
  10. G. Junker, Supersymmetric Methods in Quantum and Statistical Physics, Springer, Berlin, Germany, 1996.
  11. J. M. Fellows and R. A. Smith, “Factorization solution of a family of quantum nonlinear oscillators,” Journal of Physics A, vol. 42, no. 33, Article ID 335303, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. R. De, R. Dutt, and U. Sukhatme, “Mapping of shape invariant potentials under point canonical transformations,” Journal of Physics A, vol. 25, no. 13, pp. L843–L850, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. N. Kandirmaz and R. Sever, “Coherent states for PT-/non-PT-symmetric and non-Hermitian Morse potentials via the path integral,” Physica Scripta, vol. 81, no. 3, Article ID 035302, 2010.
  14. H. Ciftci, R. L. Hall, and N. Saad, “Asymptotic iteration method for eigenvalue problems,” Journal of Physics A, vol. 36, no. 47, pp. 11807–11816, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. N. Saad, R. L. Hall, and H. Ciftci, “The Klein-Gordon equation with the Kratzer potential in d dimensions,” Central European Journal of Physics, vol. 6, no. 3, pp. 717–729, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. Z.-Q. Ma and B.-W. Xu, “Quantum correction in exact quantization rules,” Europhysics Letters, vol. 69, no. 5, pp. 685–691, 2005. View at Publisher · View at Google Scholar · View at Scopus
  17. S.-H. Dong and M. Cruz-Irisson, “Energy spectrum for a modified Rosen-Morse potential solved by proper quantization rule and its thermodynamic properties,” Journal of Mathematical Chemistry, vol. 50, no. 4, pp. 881–892, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. M. Bag, M. M. Panja, R. Dutt, and Y. P. Varshni, “Modified shifted large-N approach to the Morse oscillator,” Physical Review A, vol. 46, no. 9, pp. 6059–6062, 1992. View at Publisher · View at Google Scholar · View at Scopus
  19. S. M. Ikhdair, “Rotational and vibrational diatomic molecule in the Klein-Gordon equation with hyperbolic scalar and vector potentials,” International Journal of Modern Physics C, vol. 20, no. 10, pp. 1563–1582, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. S. M. Ikhdair and R. Sever, “A perturbative treatment for the energy levels of neutral atoms,” International Journal of Modern Physics A, vol. 21, no. 31, pp. 6465–6476, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. S.-H. Dong, “A new approach to the relativistic schrödinger equation with central potential: Ansatz method,” International Journal of Theoretical Physics, vol. 40, no. 2, pp. 559–567, 2001. View at MathSciNet · View at Scopus
  22. S.-H. Dong, “The ansatz method for analyzing Schrödinger's equation with three anharmonic potentials in D dimensions,” Foundations of Physics Letters, vol. 15, no. 4, pp. 385–395, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  23. C. Quigg and J. L. Rosner, “Quantum mechanics with applications to quarkonium,” Physics Reports, vol. 56, no. 4, pp. 167–235, 1979. View at Scopus
  24. M. Chaichian and R. Kögerler, “Coupling constants and the nonrelativistic quark model with charmonium potential,” Annals of Physics, vol. 124, no. 1, pp. 61–123, 1980. View at Scopus
  25. G. Plante and A. F. Antippa, “Analytic solution of the Schrödinger equation for the Coulomb-plus-linear potential. I. The wave functions,” Journal of Mathematical Physics, vol. 46, no. 6, Article ID 062108, 20 pages, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. J. D. Stack, “Heavy-quark potential in SU(3) lattice gauge theory,” Physical Review D, vol. 29, no. 6, pp. 1213–1218, 1984. View at Publisher · View at Google Scholar · View at Scopus
  27. G. S. Bali, K. Schilling, and A. Wachter, “Complete O(v2) corrections to the static interquark potential from SU(3) gauge theory,” Physical Review D, vol. 56, no. 5, pp. 2566–2589, 1997. View at Scopus
  28. E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T.-M. Yan, “Erratum: Charmonium: the model,” Physical Review D, vol. 21, no. 1, p. 313, 1980. View at Publisher · View at Google Scholar · View at Scopus
  29. E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T. M. Yan, “Charmonium: comparison with experiment,” Physical Review D, vol. 21, no. 1, pp. 203–233, 1980. View at Publisher · View at Google Scholar · View at Scopus
  30. J.-L. Domenech-Garret and M.-A. Sanchis-Lozano, “Spectroscopy, leptonic decays and the nature of heavy quarkonia,” Physics Letters B, vol. 669, no. 1, pp. 52–57, 2008. View at Publisher · View at Google Scholar · View at Scopus
  31. J.-L. Domenech-Garret and M.-A. Sanchis-Lozano, “QQ-onia package: a numerical solution to the Schrödinger radial equation for heavy quarkonium,” Computer Physics Communications, vol. 180, no. 5, pp. 768–778, 2009. View at Publisher · View at Google Scholar · View at Scopus
  32. D. Bessis, E. R. Vrscay, and C. R. Handy, “Hydrogenic atoms in the external potential V(r)=gr+λr2: exact solutions and ground-state eigenvalue bounds using moment methods,” Journal of Physics A, vol. 20, no. 2, pp. 419–428, 1987. View at Publisher · View at Google Scholar · View at Scopus
  33. Z. Ghalenovi, A. A. Rajabi, and M. Hamzavi, “The heavy baryon masses in variational approach and spin-isospin dependence,” Acta Physica Polonica B, vol. 42, no. 8, pp. 1849–1859, 2011. View at Publisher · View at Google Scholar · View at Scopus
  34. M. Hamzavi and A. A. Rajabi, “Solution of Dirac equation with Killingbeck potential by using wave function ansatz method under spin symmetry limit,” Communications in Theoretical Physics, vol. 55, no. 1, pp. 35–37, 2011. View at Scopus
  35. S.-H. Dong, “On the solutions of the Schrödinger equation with some anharmonic potentials: wave function ansatz,” Physica Scripta, vol. 65, no. 4, pp. 289–295, 2002. View at Publisher · View at Google Scholar · View at Scopus
  36. M. Znojil, “The generalized continued fractions and potentials of the Lennard-Jones type,” Journal of Mathematical Physics, vol. 31, no. 8, pp. 1955–1961, 1990. View at Scopus
  37. S. M. Ikhdair and M. Hamzavi, “Spectral properties of quantum dots influenced by a confining potential model,” Physica B, vol. 407, pp. 4797–4803, 2012.
  38. A. A. Rajabi and M. Hamzavi, “Relativistic e¤ect of external magnetic and Aharonov-Bohm fields on the unequal scalar and vector Cornell model,” European Physical Journal Plus, vol. 128, pp. 5–6, 2013.
  39. S. M. Ikhdair, “A scalar charged particle in presence of magnetic and Aharonov-Bohm field plus scalar-vector Killingbeck potentials,” Few-Body Systems, vol. 54, no. 11, pp. 1987–1995, 2013. View at Publisher · View at Google Scholar
  40. A. Arda and R. Sever, “Effective-mass Klein-Gordon equation for non-PT/non-Hermitian generalized Morse potential,” Physica Scripta, vol. 82, no. 6, Article ID 065007, 2010. View at Publisher · View at Google Scholar · View at Scopus
  41. M. Hamzavi, S. M. Ikhdair, and K. E. Thylwe, “Pseudospin symmetry in the relativistic Killingbeck potential: quasi-exact solution,” Zeitschrift fur Naturforschung A, vol. 67, pp. 567–571, 2012.
  42. S.-H. Dong, Z.-Q. Ma, and G. Esposito, “Exact solutions of the Schrödinger equation with inverse-power potential,” Foundations of Physics Letters, vol. 12, no. 5, pp. 465–474, 1999. View at Scopus
  43. S.-H. Dong, “Exact solutions of the two-dimensional Schrödinger equation with certain central potentials,” International Journal of Theoretical Physics, vol. 39, no. 4, pp. 1119–1128, 2000. View at Scopus
  44. S.-H. Dong, “A new approach to the relativistic schrödinger equation with central potential: Ansatz method,” International Journal of Theoretical Physics, vol. 40, no. 2, pp. 559–567, 2001. View at Scopus
  45. W. Greiner, Relativistic Quantum Mechanics: Wave Equations, Springer, Berlin, Germany, 2000. View at MathSciNet
  46. A. D. Alhaidari, H. Bahlouli, and A. Al-Hasan, “Dirac and Klein-Gordon equations with equal scalar and vector potentials,” Physics Letters A, vol. 349, no. 1–4, pp. 87–97, 2006. View at Publisher · View at Google Scholar · View at Scopus
  47. R. Khordad, “Effects of magnetic field and geometrical size on the interband light absorption in a quantum pseudodot system,” Solid State Sciences, vol. 12, no. 7, pp. 1253–1256, 2010. View at Publisher · View at Google Scholar · View at Scopus
  48. R. Khordad, “Simultaneous effects of temperature and pressure on the donor binding energy in a V-groove quantum wire,” Superlattices and Microstructures, vol. 47, no. 3, pp. 422–431, 2010. View at Publisher · View at Google Scholar · View at Scopus
  49. A. Çetin, “A quantum pseudodot system with a two-dimensional pseudoharmonic potential,” Physics Letters A, vol. 372, no. 21, pp. 3852–3856, 2008. View at Publisher · View at Google Scholar · View at Scopus
  50. S. M. Ikhdair, M. Hamzavi, and R. Sever, “Spectra of cylindrical quantum dots: the effect of electrical and magnetic fields together with AB flux field,” Physica B, vol. 407, pp. 4523–4529, 2012.
  51. S. M. Ikhdair and M. Hamzavi, “A quantum pseudodot system with two-dimensional pseudoharmonic oscillator in external magnetic and Aharonov-Bohm fields,” Physica B, vol. 407, pp. 4198–4207, 2012.
  52. S. M. Ikhdair and M. Hamzavi, “Effects of extermal fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction,” Chinese Physics B, vol. 21, no. 11, Article ID 110302, 2012. View at Publisher · View at Google Scholar
  53. Y. Xu, S. He, and C.-S. Jia, “Approximate analytical solutions of the Klein-Gordon equation with the Pöschl-Teller potential including the centrifugal term,” Physica Scripta, vol. 81, no. 4, Article ID 045001, 2010. View at Publisher · View at Google Scholar · View at Scopus
  54. R. L. Liboff, Introductory Quantum Mechanics, Addison-Wesley, San Francisco, Calif, USA, 2003.
  55. G. Chen, Z.-D. Chen, and Z.-M. Lou, “Bound states of the Klein-Gordon and Dirac equation for scalar and vector pseudoharmonic oscillator potentials,” Chinese Physics, vol. 13, no. 3, pp. 279–282, 2004. View at Publisher · View at Google Scholar · View at Scopus
  56. S. M. Ikhdair and J. Abu-Hasna, “Quantization rule solution to the Hulthén potential in arbitrary dimension with a new approximate scheme for the centrifugal term,” Physica Scripta, vol. 83, no. 2, Article ID 025002, 2011. View at Publisher · View at Google Scholar · View at Scopus
  57. S. M. Ikhdair and R. Sever, “Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules,” Journal of Mathematical Chemistry, vol. 45, no. 4, pp. 1137–1152, 2009. View at Publisher · View at Google Scholar · View at Scopus
  58. C. Berkdemir, A. Berkdemir, and J. Han, “Bound state solutions of the Schrödinger equation for modified Kratzer's molecular potential,” Chemical Physics Letters, vol. 417, no. 4–6, pp. 326–329, 2006. View at Publisher · View at Google Scholar · View at Scopus
  59. G. Chen, Z.-D. Chen, and P.-C. Xuan, “Semiclassical methods to the Klein-Gordon equation with the unequal scalar and vector potentials,” Physica Scripta, vol. 74, no. 3, pp. 367–370, 2006. View at Publisher · View at Google Scholar · View at Scopus
  60. S. M. Ikhdair and R. Sever, “Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthén potentials,” Physica Scripta, vol. 79, no. 3, Article ID 035002, 2009. View at Publisher · View at Google Scholar · View at Scopus
  61. S. M. Ikhdair, “Bound states of the Klein-Gordon for exponential type potentials in D-dimensions,” Journal of Quantum Information Science, vol. 1, no. 2, pp. 73–86, 2011.
  62. M. Hamzavi, S. M. Ikhdair, and K. E. Thylwe, “Spinless particles in the field of unequal scalar-vector Yukawa potentials,” Chinese Physics B, vol. 22, no. 4, Article ID 040301, 6 pages, 2013.
  63. F. Domínguez-Adame, “Bound states of the Klein-Gordon equation with vector and scalar Hulthén-type potentials,” Physics Letters A, vol. 136, no. 4-5, pp. 175–177, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  64. S. M. Ikhdair and B. J. Falaye, “A charged spinless particles in scalar-vector harmonic oscillators with uniform magnetic and Aharonov-Bohm flux fields,” Journal of the Association of Arab Universities for Basic and Applied Sciences. In press.