International Journal of Theoretical Physics

, Volume 46, Issue 6, pp 1643–1665 | Cite as

Exact Polynomial Solution of \({\cal P}{\cal T}$/Non-${\cal P}{\cal T}\)- Symmetric and Non-Hermitian Modified Woods–Saxon Potential by the Nikiforov–Uvarov Method

Article

Abstract

Using the Nikiforov–Uvarov (NU) method, the bound state energy eigenvalues and eigenfunctions of the \({\cal P{\cal T}}$-/non-${\cal P}{\cal T}\)-symmetric and non-Hermitian modified Woods–Saxon (WS) model potential with the real and complex-valued energy levels are obtained in terms of the Jacobi polynomials. According to the \({\cal P}{\cal T}\)-symmetric quantum mechanics, we exactly solved the time-independent Schrödinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement with the ones obtained before.

Keywords

energy eigenvalues and eigenfunctions modified WS potential \({\cal P}{\cal T}\)-symmetry non-Hermitian potential NU method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahmed, Z. (1991). Physics Letters A 157, 1.CrossRefADSGoogle Scholar
  2. Ahmed, Z. (1993). Physical Review A 47, 4757.CrossRefADSGoogle Scholar
  3. Ahmed, Z. (2001a). Physics Letters A 282, 343.MATHCrossRefGoogle Scholar
  4. Ahmed, Z. (2001b). Physics Letters A 290, 19.MATHCrossRefADSGoogle Scholar
  5. Aktaş, M. and Sever, R. (2004). Journal of Molecular Structure 710, 219.Google Scholar
  6. Arai, A. (1991). J. Math. Anal. Appl. 158, 63.MATHCrossRefMathSciNetGoogle Scholar
  7. Bagchi, B. and Quesne, C. (2000). Physics Letters A 273, 285.MATHCrossRefMathSciNetADSGoogle Scholar
  8. Barclay, D. T., et al. (2002). Physics Letters A 305, 231.CrossRefMathSciNetGoogle Scholar
  9. Barton, G. (1986). Annals of Physics 166, 322.CrossRefMathSciNetADSGoogle Scholar
  10. Bekmezci, A., Ikhdair, S. M., Magdy, M. A., and Sever, R. (1993). Hadronic Journal 16, 339.Google Scholar
  11. Bender, C. M., Boettcher, S., and Meisenger, P. N. (1999a). Journal of Mathematical Physics 40, 2201.MATHCrossRefADSGoogle Scholar
  12. Bender, C. M., Dunne, G. V., and Meisenger, P. N. (1999b). Physics Letters A 252, 272.MATHCrossRefADSGoogle Scholar
  13. Bender, C. M., Dunne, G. V., Meisenger, P. N., and şimşek, M. (2001). Physics Letters A 281, 311.MATHCrossRefMathSciNetADSGoogle Scholar
  14. Bender, C. M., Brody, D. C., and Jones, H. F. (2002). Physical Review Letters 89, 270402.CrossRefMathSciNetGoogle Scholar
  15. Bender, C. M. and Boettcher, S. (1998a). Journal of Physics A 31, 1273.CrossRefGoogle Scholar
  16. Bender, C. M. and Boettcher, S. (1998b). Physical Review Letters 80, 5243.MATHCrossRefMathSciNetADSGoogle Scholar
  17. Berkdemir, C., Berkdemir, A., and Sever, R. (2005). Physical Review C 72, 027001.CrossRefADSGoogle Scholar
  18. Berkdemir, A., Berkdemir, C., and Sever, R. (2006a). Modern Physics Letters A 21, 2087.MATHCrossRefMathSciNetADSGoogle Scholar
  19. Berkdemir, C., Berkdemir, A., and Sever, R. (2006b). Nuclear Physics A 770 32.CrossRefADSGoogle Scholar
  20. Berkdemir, C., Berkdemir, A., and Han, J. (2006c). Chemical Physics Letters 417, 326.CrossRefGoogle Scholar
  21. Berkdemir, C. and Han, J. (2005). Chemical Physics Letters 409, 203.CrossRefADSGoogle Scholar
  22. Brack, M. (1993). Rev. Mod. Phys. 65, 677.CrossRefADSGoogle Scholar
  23. Bulgac, A. and Lewenkopf, C. (1993). Phys. Rev. Lett. 71, 4130.CrossRefADSGoogle Scholar
  24. Cannato, F., Junker, G., and Trost, J. (1998). Physics Letters A 246, 219.CrossRefMathSciNetADSGoogle Scholar
  25. Chamon, L. C., et al. (1996). Nuclear Physics A 597, 253.CrossRefMathSciNetADSGoogle Scholar
  26. Christensen, R. P. and Winther, A. (1976). Physics Letters B 65, 19.CrossRefADSGoogle Scholar
  27. Costa, L. S., Prudenter, F. V., Acioli, P. H., Soares Neto, J. J., and Vianna, J. D. M. (1999). Journal of Physics B 32, 2461.CrossRefADSGoogle Scholar
  28. Delabaere, E. and Trinh, D. T. (2000a). Journal of Physics A 33, 8771.MATHCrossRefMathSciNetGoogle Scholar
  29. Delabaere, E. and Trinh, D. T. (2000b). Journal of Physics A 33, 8771.MATHCrossRefMathSciNetGoogle Scholar
  30. Eğrifes, H., Demirhan, D., and Büyükkiliç, F. (1999a). Physica Scripta 59, 90.CrossRefADSGoogle Scholar
  31. Eğrifes, H., Demirhan, D., and Büyükkiliç, F. (1999b). Physica Scripta 60, 195.CrossRefADSGoogle Scholar
  32. Eğrifes, H. and Sever, R. (2005). Physics Letters A 344, 117.CrossRefMathSciNetADSGoogle Scholar
  33. Fernández, F. M., Guardiola, R., Ros, J., and Znojil, M. (1998). Journal of Physics A 31, 10105.MATHCrossRefGoogle Scholar
  34. Filho, E. D. and Ricotta, R. M. (1995). Modern Physics Letters A 10, 1613.CrossRefADSGoogle Scholar
  35. Flügge, S. (1971). Practical Quantum Mechanics I, Springer-Verlag, Berlin.Google Scholar
  36. Hagino, K., et al. (2001). [arXiv:nucl-th/0110065] A talk given at the 4th Italy-Japan Symposium on Heavy-Ion Physics Tokyo, Japan.Google Scholar
  37. Hamamato, I., Lukyanov, S., and Zhang, X. Z. (2001). Nuclear Physics A 683, 255.CrossRefADSGoogle Scholar
  38. Ikhdair, S. M., et al. (1992). Turkish Journal of Physics 16, 510.Google Scholar
  39. Ikhdair, S. M., et al. (1993a) Turkish Journal of Physics 17, 474.Google Scholar
  40. Ikhdair, S. M., et al. (1993b). Hadronic Journal 16, 57.Google Scholar
  41. Ikhdair, S. M., et al. (1994a). Hadronic Journal 17, 151.Google Scholar
  42. Ikhdair, S. M., et al. (1994b). Hadronic Journal Supplement 19, 417.Google Scholar
  43. Ikhdair, S. and Sever, R. (1992a). Hadronic Journal 15, 375.Google Scholar
  44. Ikhdair, S. M. and Sever, R. (1992b). Zeitschrift fur Physik C (Particles and Fields) 56, 155.CrossRefGoogle Scholar
  45. Ikhdair, S. M. and Sever, R. (1992c). Hadronic Journal 15, 389.Google Scholar
  46. Ikhdair, S. M. and Sever, R. (1993a). Zeitschrift fur Physik C (Particles and Fields) C 58, 153.CrossRefGoogle Scholar
  47. Ikhdair, S. M. and Sever, R. (1993b). Zeitschrift für Physik 28, 1.CrossRefGoogle Scholar
  48. Ikhdair, S. M. and Sever, R. (2003). International Journal of Modern Physics A 18, 4215.MATHCrossRefADSGoogle Scholar
  49. Ikhdair, S. M. and Sever, R. (2004). International Journal of Modern Physics A 19, 1771.CrossRefADSGoogle Scholar
  50. Ikhdair, S. M. and Sever, R. (2005a). International Journal of Modern Physics A 20, 4035.CrossRefADSGoogle Scholar
  51. Ikhdair, S. M. and Sever, R. (2005b). [arXiv:quant-ph/0511209] to appear in International Journal of Modern Physics A.Google Scholar
  52. Ikhdair, S. M. and Sever, R. (2005c). International Journal of Modern Physics A 20, 6509.MATHCrossRefADSGoogle Scholar
  53. Ikhdair, S. M. and Sever, R. (2005d). [arXiv:quant-ph/0508009] to appear in Journal of Mathematical and Chemistry.Google Scholar
  54. Ikhdair, S. M. and Sever, R. (2005e). [arXiv:hep-ph/0504107] to appear in International Journal of Modern Physics A.Google Scholar
  55. Ikhdair, S. M. and Sever, R. (2006a). International Journal of Modern Physics A 21, 2191.CrossRefADSGoogle Scholar
  56. Ikhdair, S. M. and Sever, R. (2006b). [arXiv:quant-ph/0604073] to appear in Journal of Mathematical Chemistry.Google Scholar
  57. Ikhdair, S. M. and Sever, R. (2006c). International Journal of Modern Physics A 21, 3989.MATHCrossRefADSGoogle Scholar
  58. Ikhdair, S. M. and Sever, R. (2006d). [arXiv:quant-ph/0604078] to appear in Journal of Mathematical Chemistry.Google Scholar
  59. Ikhdair, S. M. (2005). [arXiv:hep-ph/0504176] to appear in International Journal of Modern Physics E.Google Scholar
  60. Jaminon, M., Jeukenne, J. P., and Mahaux, C. (1986). Physical Review C 34, 468.CrossRefADSGoogle Scholar
  61. Japaridze, G. S. (2002). Journal of Physics 35, 1709.MATHMathSciNetGoogle Scholar
  62. Jia, C. S., Zeng, X. L., and Sun, L. T. (2002). Physics Letters A 294, 185.MATHCrossRefMathSciNetADSGoogle Scholar
  63. Khare, A. and Mandal, B. P. (2000). Physics Letters A 272, 53.CrossRefMathSciNetADSGoogle Scholar
  64. Khare, A. and Sukhatme, U. P. (1988). Journal of Physics A 21, L501.CrossRefMathSciNetADSGoogle Scholar
  65. Kretschmer, R. and Szymanowski, L. (2001a). [arXiv:quant-ph/0105054].Google Scholar
  66. Lévai, G. and Znojil, M. (2002). Journal of Physics A 35, 8793.MATHCrossRefGoogle Scholar
  67. Landau, L. D. and Lifshitz, E. M. (1958). Quantum Mechanics, Pergamon Press, London.MATHGoogle Scholar
  68. Macrobert, T. M. (1962). Foundations of a Complex Variables, London, Macmillan.Google Scholar
  69. Magnus, W., Oberhettinger, F., and Soni, R. P. (1966). Formulas and Theorems for the Special Function of Mathematical Physics, 3rd edn. Berlin, Springer.Google Scholar
  70. Mezincescu, G. A. (2000). Journal of Physics A 33, 4911.MATHCrossRefMathSciNetGoogle Scholar
  71. Mondal, C. K., Maji, K., and Bhattacharyya, S. P. (2001). Physics Letters A 291, 203.MATHCrossRefMathSciNetADSGoogle Scholar
  72. Morse, P. M. and Feshbach, H. (1953). Methods of Theoretical Physics, McGraw-Hill Book Company, Ltd. New York. pp. 1650–1660.MATHGoogle Scholar
  73. Mostafazadeh, A. (2002a). Journal of Mathematical Physics 43, 205.MATHCrossRefMathSciNetADSGoogle Scholar
  74. Mostafazadeh, A. (2002b). Journal of Mathematical Physics 43, 2814.MATHCrossRefMathSciNetADSGoogle Scholar
  75. Mostafazadeh, A. (2002c). Journal of Mathematical Physics 43, 3944.MATHCrossRefMathSciNetADSGoogle Scholar
  76. Nikiforov, A. F. and Uvarov, V. B. (1988). Special Functions of Mathematical Physics, Birkhauser, Basel.MATHGoogle Scholar
  77. Prudrinkov, A. P., Brychkov, Y. A., and Marichev, O. I. (1986). Integrals and Series, New York, Gordon and Breach.Google Scholar
  78. Sahu, B., Agarwalla, S. K., and Shastry, C. S. (2002). Journal of Physics A 35, 4349.MATHCrossRefMathSciNetGoogle Scholar
  79. Sezgo, G. (1939). Orthogonal Polynomials, American Mathematical Society, New York.Google Scholar
  80. Shin, K. C. (2001). Journal of Mathematical Physics 42, 2513.MATHCrossRefMathSciNetADSGoogle Scholar
  81. Silva, C. P., et al. (2001). Nuclear Physics A 679, 287.CrossRefADSGoogle Scholar
  82. şimşek, M. and Eğrifes, H. (2004). Journal of Physics A (Mathematical and General) 37, 4379.CrossRefMathSciNetADSGoogle Scholar
  83. Taylor, B. N. (1984). Physical Constants Table, Reviews of Modern Physics 56, 531.Google Scholar
  84. Yasuk, F., Berkdemir, C., Berkdemir, A., and önem, C. (2005). Physica Scripta 71, 340.CrossRefADSGoogle Scholar
  85. Yeşiltaş, ö., şimşek, M., Sever, R., and Tezcan, C. (2003). Physica Scripta 67, 472.CrossRefMathSciNetADSGoogle Scholar
  86. Znojil, M. and Tater, M. (2001). Journal of Physics A 34, 1793.MATHCrossRefMathSciNetGoogle Scholar
  87. Znojil, M. (1999). Physics Letters A 264, 108.MATHCrossRefMathSciNetADSGoogle Scholar
  88. Znojil, M. (2000). Journal of Physics A 33, 4203.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of PhysicsNear East UniversityNicosia, Mersin 10Turkey
  2. 2.Department of PhysicsMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations