×

Approximate eigenvalue and eigenfunction solutions for the generalized Hulthén potential with any angular momentum. (English) Zbl 1132.81352

Summary: An approximate solution of the Schrödinger equation for the generalized Hulthén potential with non-zero angular quantum number is solved. The bound state energy eigenvalues and eigenfunctions are obtained in terms of Jacobi polynomials. The Nikiforov-Uvarov method is used in the computations. We have considered the time-independent Schrödinger equation with the associated form of Hulthén potential which simulate the effect of the centrifugal barrier for any \(l\)-state. The energy levels of the used Hulthén potential gives satisfactory values for the non-zero angular momentum as the generalized Hulthén effective potential.

MSC:

81V55 Molecular physics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hulthén L., Ark. Mat. Astron. Fys. 28 A (1942) 5; ibid., Ark. Mat. Astron. Fys. 29 B (1942) 1.
[2] Eckart C.,(1930). Phys. Rev 35: 1303 · JFM 56.0750.03 · doi:10.1103/PhysRev.35.1303
[3] Varshni Y.P., (1990). Phys. Rev A 41: 4682 · doi:10.1103/PhysRevA.41.4682
[4] Lam C.S., Varshni Y.P., (1971). Phys. Rev. A 4: 1875 · doi:10.1103/PhysRevA.4.1875
[5] Flügge S., (1974). Practical Quantum Mechanics. Springer-Verlag, Berlin
[6] C.Lai S., Lim W.C., (1980). Phys. Lett. A 78: 335 · doi:10.1016/0375-9601(80)90388-6
[7] Dutt R., Mukherji U., (1982). Phys. Lett, A 90: 395 · doi:10.1016/0375-9601(82)90793-9
[8] Patil S.H., (1984). J. Phys. A 17: 575 · Zbl 0581.05042 · doi:10.1088/0305-4470/17/3/019
[9] Popov V.S., Weiberg V.M., (1985). Phys. Lett. A 107: 371 · doi:10.1016/0375-9601(85)90692-9
[10] Roy B., Roychoudhury R., (1987). J. Phys. A 20: 3051 · doi:10.1088/0305-4470/20/10/048
[11] Tang A.Z., Chan F.T., (1987). Phys. Rev. A 35: 911 · doi:10.1103/PhysRevA.35.911
[12] Lai C.H., (1987). J. Math. Phys 28: 1801 · Zbl 0625.34017 · doi:10.1063/1.527439
[13] Matthys P., De H., (1988). Phys. Rev. A 38: 1168 · doi:10.1103/PhysRevA.38.1168
[14] Laha U., Bhattacharyya C., Roy K., Talukdar B., (1988). Phys. Rev. C 38: 558 · doi:10.1103/PhysRevC.38.558
[15] Talukdar B., Das U., Bhattacharyya C., Bera P.K., (1992). J. Phys. A 25: 4073 · Zbl 0757.34070 · doi:10.1088/0305-4470/25/14/021
[16] Filho E.D., Ricotta R.M., (1995). Mod. Phys. Lett. A 10: 1613 · doi:10.1142/S0217732395001733
[17] Cooper F., Khare A., Sukhatme U., (1995). Phys. Rep 251: 267 · doi:10.1016/0370-1573(94)00080-M
[18] Gönül B., Özer O., Cançelik Y., Koçak M., (2000). Phys. Lett. A 275: 238 · Zbl 1115.81349 · doi:10.1016/S0375-9601(00)00590-9
[19] Nikiforov A.F., Uvarov V.B., (1988). Special Functions of Mathematical Physics. Birkhauser, Basel · Zbl 0624.33001
[20] Yeşiltaş Ö., Şimşek M., Sever R., Tezcan C., (2003). Physica Scripta 67: 472 · Zbl 1045.35060 · doi:10.1238/Physica.Regular.067a00472
[21] Berkdemir C., Berkdemir A., Sever R., Phys. Rev. C 72 (2005) 027001; Berkdemir A., Berkdemir C., R. Sever [arXiv:quant-ph/0410153].
[22] Berkdemir C., Han J., Chem. Phys. Lett. 409 (2005) 203; Berkdemir C., Berkdemir A., Han J., Chem. Phys. Letters 417 (2006) 326
[23] M. Aktaş and Sever R., J. Math. Chem. 37 (2005) 139; Faridfathi G., Sever R., Metin Aktaş, J. Math. Chem. 38 (2005) 533
[24] Greene R.L., Aldrich C., (1976). Phys. Rev. A 14: 2363 · doi:10.1103/PhysRevA.14.2363
[25] Şimşek M., Eğrifes H., (2004). J. Phys. A. Math. Gen 37: 4379 · Zbl 1053.81023 · doi:10.1088/0305-4470/37/15/007
[26] Gendenshtein L., (1983). JETP Lett 38: 356
[27] Filho E.D., Ricotta R.M., (1995). Mod. Phys. Lett. A10: 1613 · doi:10.1142/S0217732395001733
[28] Sezgo G., (1939). Orthogonal Polynomials. American Mathematical Society, New York
[29] Ikhdair S.M., Sever R., To appear in Phys. Rev. C.
[30] Aktaş M., Sever R., (2004). J. Molec. Struc 710: 219
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.