×

A particular solution of Heun equation for Hulthen and Woods-Saxon potentials. (English) Zbl 1322.34005

Summary: A particular solution of the Heun equation is derived by making use of the Nikiforov-Uvarov (NU) method which provides exact solutions for general hypergeometric equations and eigenvalues together with eigenfunctions. One to one correspondence (isomorphism) of the aforesaid equation with the radial Schrödinger equation is emphasized and also physical counterparts of the parameters in this equation are put forward by introducing solutions for two different potential functions (Hulthen and Woods-Saxon potentials).

MSC:

34A05 Explicit solutions, first integrals of ordinary differential equations
34A30 Linear ordinary differential equations and systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ferreira, Integr. Transf. Spec. F 21 pp 839– (2010) · Zbl 1250.34012 · doi:10.1080/10652461003747999
[2] Gurappa, J. Phys. A-Math Gen. 37 pp 605– (2004) · Zbl 1068.34003 · doi:10.1088/0305-4470/37/46/L01
[3] K. Takemura arXiv:1106.1543v3 [math CA] 2012
[4] M. Hortaçsu arXiv:1101.0471v1 [math-ph] 2011
[5] Barton, Ann. Phys-New York 166 pp 322– (1986) · doi:10.1016/0003-4916(86)90142-9
[6] Flügge, Practical Quantum Mechanics II (1971) · Zbl 1400.81003 · doi:10.1007/978-3-642-65114-4
[7] Landau, Quantum Mechanics (1958)
[8] Morse, Methods of Theoretical Physics (1953) · Zbl 0051.40603
[9] Sahu, J. Phys. A-Math Gen. 35 pp 4349– (2002) · Zbl 1045.81554 · doi:10.1088/0305-4470/35/19/314
[10] Khare, J. Phys. A-Math Gen. 21 pp 501– (1988) · doi:10.1088/0305-4470/21/9/005
[11] Ahmed, Phys. Lett. A 157 pp 1– (1991) · doi:10.1016/0375-9601(91)90399-S
[12] Jia, Phys. Lett. A 294 pp 185– (2002) · Zbl 0985.81031 · doi:10.1016/S0375-9601(01)00840-4
[13] Lévai, J. Phys. A-Math Gen. 35 pp 8793– (2002) · Zbl 1044.81578 · doi:10.1088/0305-4470/35/41/311
[14] Yeşiltaş, Phys. Scripta. 67 pp 472– (2003) · Zbl 1045.35060 · doi:10.1238/Physica.Regular.067a00472
[15] Znojil, Phys. Lett. A 264 pp 108– (1999) · Zbl 0949.81020 · doi:10.1016/S0375-9601(99)00805-1
[16] Ahmed, Phys. Lett. A 290 pp 19– (2001) · Zbl 1020.81016 · doi:10.1016/S0375-9601(01)00622-3
[17] Bender, J. Phys. A-Math Gen. 31 pp 273– (1998) · Zbl 0929.34074 · doi:10.1088/0305-4470/31/14/001
[18] Znojil, J. Phys. A-Math Gen. 33 pp 4203– (2000) · Zbl 0954.81060 · doi:10.1088/0305-4470/33/22/320
[19] Eğrifes, Phys. Scripta. 60 pp 195– (1999a) · Zbl 0943.81009 · doi:10.1238/Physica.Regular.060a00195
[20] Eğrifes, Phys. Scripta. 59 pp 90– (1999b) · Zbl 1063.81532 · doi:10.1238/Physica.Regular.059a00090
[21] Eğrifes, Phys. Lett. A 344 pp 117– (2005) · Zbl 1194.81064 · doi:10.1016/j.physleta.2005.06.061
[22] Şimşek, J. Phys. A-Math Gen. 37 pp 4379– (2004) · Zbl 1053.81023 · doi:10.1088/0305-4470/37/15/007
[23] Yasuk, Phys. Scripta. 71 pp 340– (2005) · doi:10.1238/Physica.Regular.071a00340
[24] Nikiforov, Special Functions of Mathematical Physics (1988) · doi:10.1007/978-1-4757-1595-8
[25] Pahlavani, Theoretical Concepts of Quantum Mechanics (2012) · doi:10.5772/2075
[26] Szego, Orthogonal Polynomials (1939) · doi:10.1090/coll/023
[27] Ikhdair, Int. J. Theor. Phys. 46 pp 2384– (2007) · Zbl 1133.81017 · doi:10.1007/s10773-007-9356-8
[28] Berkdemir, Mod. Phys. Lett. A 21 pp 2087– (2006) · Zbl 1126.81023 · doi:10.1142/S0217732306019906
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.