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Volume 9, Issue 4 (Aug 2011)

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Approximate analytical solutions for arbitrary l-state of the Hulthén potential with an improved approximation of the centrifugal term

Jerzy Stanek
  • Faculty of Chemistry, Adam Mickiewicz University, 60-780, Poznań, Poland
  • Email:
Published Online: 2011-06-04 | DOI: https://doi.org/10.2478/s11532-011-0050-6

Abstract

An approximate analytical solution of the radial Schrödinger equation for the generalized Hulthén potential is obtained by applying an improved approximation of the centrifugal term. The bound state energy eigenvalues and the normalized eigenfunctions are given in terms of hypergeometric polynomials. The results for arbitrary quantum numbers n r and l with different values of the screening parameter δ are compared with those obtained by the numerical method, asymptotic iteration, the Nikiforov-Uvarov method, the exact quantization rule, and variational methods. The results obtained by the method proposed in this work are in a good agreement with those obtained by other approximate methods.

Keywords: Hulthén potential; Energy eigenvalues and eigenfunctions; Centrifugal term

  • [1] L. Hulthén, Ark. Mat. Astron. Fys. A 28, 5 (1942)

  • [2] L. Hulthén, Ark. Mat. Astron. Fys. B 29, 1 (1942)

  • [3] S. Flügge, Practical Quantum Mechanics (Springer-Verlag, Berlin Heidelberg, 1994)

  • [4] O.L. de Lange, Am. J. Phys. 59, 151 (1991) http://dx.doi.org/10.1119/1.16596 [Crossref]

  • [5] M.R. Setare, E. Karimi, Int. J. Theor. Phys. 46, 1381 (2007) http://dx.doi.org/10.1007/s10773-006-9276-z [Crossref]

  • [6] R.L. Greene, C. Aldrich, Phys. Rev. A 14, 2363 (1976) http://dx.doi.org/10.1103/PhysRevA.14.2363 [Crossref]

  • [7] O. Bayrak, G. Kocak, I Boztosun, J. Phys. A: Math. Gen. 39, 11521 (2006) http://dx.doi.org/10.1088/0305-4470/39/37/012 [Crossref]

  • [8] S.M. Ikhdair, R. Sever, J. Math. Chem. 42, 461 (2007) http://dx.doi.org/10.1007/s10910-006-9115-8 [Crossref]

  • [9] W.C. Qiang, S.H. Dong, Phys. Lett. A 368, 13 (2007) http://dx.doi.org/10.1016/j.physleta.2007.03.057 [Crossref]

  • [10] W.C. Qiang, Y. Gao, R.S. Zhou, Cent. Eur. J. Phys. 6, 356 (2008) http://dx.doi.org/10.2478/s11534-008-0041-1 [Crossref]

  • [11] C.Y. Chen, F.L. Lu, D.-S. Sun, Cent. Eur. J. Phys. 6, 884 (2008) http://dx.doi.org/10.2478/s11534-008-0099-9 [Crossref]

  • [12] C.S. Jia, J.Y. Liu, P.Q. Wang, Phys. Lett. A 372, 4779 (2008) http://dx.doi.org/10.1016/j.physleta.2008.05.030 [Crossref]

  • [13] S.M. Ikhdair, Eur. Phys. J. A 39, 307 (2009) http://dx.doi.org/10.1140/epja/i2008-10715-2 [Crossref]

  • [14] V.C. Aguilera-Navarro, E. Ley-Koo, S. Mateos-Cortes, Rev. Mex. Fis. 43, 413 (1998)

  • [15] S.M. Ikhdair, R. Sever, J. Math. Chem. 42, 461 (2006) http://dx.doi.org/10.1007/s10910-006-9115-8 [Crossref]

  • [16] O. Bayrak, G. Kocak, I. Boztosun, J. Phys. A: Math Gen. 39, 11521 (2006) http://dx.doi.org/10.1088/0305-4470/39/37/012 [Crossref]

  • [17] B. Gönül, O. Özer, Y. Cançelik, M. Koçak, Phys. Lett. A 275, 238 (2000) http://dx.doi.org/10.1016/S0375-9601(00)00590-9 [Crossref]

  • [18] A.Z. Tang, F.T. Chan, Phys. Rev. A 35, 911 (1987) http://dx.doi.org/10.1103/PhysRevA.35.911 [Crossref]

  • [19] M. Badawi, N. Bessis, G. Bessis, J. Phys. B: Atom. Molec. Phys. 5, L157 (1972) http://dx.doi.org/10.1088/0022-3700/5/8/004 [Crossref]

  • [20] J. Lu, Phys. Scr. 72, 349 (2005) http://dx.doi.org/10.1238/Physica.Regular.072a00349 [Crossref]

  • [21] S.M. Ikhdair, R. Sever, Ann. Phys. 18, 189 (2009) http://dx.doi.org/10.1002/andp.200810349 [Crossref]

  • [22] D. Schiöberg, Mol. Phys. 59, 1123 (1989) http://dx.doi.org/10.1080/00268978600102631 [Crossref]

  • [23] S.M. Ikhdair, R. Sever, arXiv:0807.2085v1 (2008) [Web of Science]

  • [24] Y.P. Varshni, Phys. Rev. A 41, 4682 (1990) http://dx.doi.org/10.1103/PhysRevA.41.4682 [Crossref]

  • [25] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover Publications, New York, 1972)

  • [26] G.F. Wei, Z.Z. Zhen, S.H. Dong, Cent. Eur. J. Phys. 7, 175 (2009) http://dx.doi.org/10.2478/s11534-008-0143-9 [Crossref]

About the article

Published Online: 2011-06-04

Published in Print: 2011-08-01



Citation Information: Open Chemistry, ISSN (Online) 2391-5420, DOI: https://doi.org/10.2478/s11532-011-0050-6. Export Citation

© 2011 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

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