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

• Autorzy: Jerzy Stanek
• Języki publikacji: EN

Abstrakty

EN

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. [...]

Słowa kluczowe

EN

Hulthén potential; Energy eigenvalues and eigenfunctions; Centrifugal term

• Czasopismo: Open Chemistry
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 737-742

Daty

wydano

2011-08-01

online

2011-06-04

Twórcy

autor

Jerzy Stanek

• Faculty of Chemistry, Adam Mickiewicz University, 60-780, Poznań, Poland,

Bibliografia

• [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) [WoS]
• [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]

Identyfikatory

DOI

10.2478/s11532-011-0050-6