Exact solutions of the Klein-Gordon equation for the Scarf-type potential via Nikiforov-Uvarov method. (English) Zbl 1190.81042
Summary: We present the exact solutions of the one-dimensional Klein-Gordon equation for the Scarf-type potential with equal scalar and vector potentials. Exact solutions and corresponding energy eigenvalues equation are obtained using Nikiforov-Uvarov mathematical method for the s-wave bound state. The PT-symmetry and Hermiticity for this potential are also considered. It is shown that the obtained results of the Scarf-type potential are reduced to the results of the well-known potentials in the special cases.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81U15 | Exactly and quasi-solvable systems arising in quantum theory |
| 81Q80 | Special quantum systems, such as solvable systems |
References:
| [1] | Volodin, B.A., Khapayev, A.M.: Comput. Math. Math. Phys. 31, 69 (1991) |
| [2] | Ikhdair, S.M.: Chin. Phys. 3, 291 (2008) |
| [3] | Abdel-Rahman, R.G.: Chin. Phys. 5, 495 (2008) |
| [4] | Hong-Sheng, H., Jiang, C., Kong-Qing, Y.: Chin. Phys. 14, 1926 (2005) · doi:10.1088/1009-1963/14/10/002 |
| [5] | Simsek, M., Egrifes, H.: J. Phys. Lond. Math. Gen. 37, 4379 (2004) · Zbl 1053.81023 · doi:10.1088/0305-4470/37/15/007 |
| [6] | Dominguez-Adame, F.: Phys. Lett. A 136, 175 (1989) · doi:10.1016/0375-9601(89)90555-0 |
| [7] | Min-Cang, Z., Zhen-Bang, W.: Chin. Phys. 16, 1863 (2007) · doi:10.1088/1009-1963/16/7/010 |
| [8] | Qiang, Z., Ping, Y., Lun-Xun, G.: Chin. Phys. 15, 35 (2006) · doi:10.1088/1009-1963/15/1/006 |
| [9] | Min-Cang, Z., Zhen-Bang, W.: Chin. Phys. Lett. 22, 2994 (2005) · doi:10.1088/0256-307X/22/12/003 |
| [10] | Yasuk, F., Durmus, A., Boztosun, I.: J. Math. Phys. 47, 082302 (2006) · Zbl 1112.81034 · doi:10.1063/1.2227258 |
| [11] | Motavali, H.: Mod. Phys. Lett. A 24, 1227 (2009) · Zbl 1170.81366 · doi:10.1142/S0217732309028941 |
| [12] | Rezaei Akbarieh, A., Motavali, H.: Mod. Phys. Lett. A 23, 3009 (2008) |
| [13] | Chen, G.: Mod. Phys. Lett. A 19, 2009 (2004) · Zbl 1076.81506 · doi:10.1142/S0217732304014677 |
| [14] | Guo, J.Y., Fang, X.Z., Xu, F.X.: Phys. Rev. A 66, 2105 (2002) |
| [15] | Chen, G.: Acta Phys. Sin. 53, 680 (2004) |
| [16] | Chen, G.: Acta Phys. Sin. 50, 1651 (2001) |
| [17] | Chen, G.: Phys. Lett. A 328, 16 (2004) · Zbl 1134.81351 · doi:10.1016/j.physleta.2004.06.034 |
| [18] | Diao, Y.F., Yi, L.Z., Jia, C.S.: Phys. Lett. A 332, 157 (2004) · Zbl 1123.35343 · doi:10.1016/j.physleta.2004.09.051 |
| [19] | Zhao, X.Q., Jia, C.S., Yang, Q.B.: Phys. Lett. A 337, 189 (2005) |
| [20] | Qiang, W.C.: Chin. Phys. 13, 571 (2004) · doi:10.1088/1009-1963/13/12/025 |
| [21] | Chen, G., Chen, Z.D., Lou, Z.M.: Chin. Phys. 13, 279 (2004) · doi:10.1088/1009-1963/13/11/034 |
| [22] | Nikiforov, A.F., Uvarov, V.B.: Special Functions of Mathematical Physics. Birkhauser, Basel (1988) · Zbl 0624.33001 |
| [23] | Bender, C.M., Boettcher, S.: Phys. Rev. Lett. 80, 5243 (1998) · Zbl 0947.81018 · doi:10.1103/PhysRevLett.80.5243 |
| [24] | Bender, C.M.: J. Math. Phys. 40, 2201 (1999) · Zbl 1057.81512 · doi:10.1063/1.532860 |
| [25] | Bender, C.M., Brody, D.C., Jones, H.F.: Phys. Rev. Lett. 89, 270401 (2002) · Zbl 1267.81234 · doi:10.1103/PhysRevLett.89.270401 |
| [26] | Bender, C.M., et al.: J. Phys. A 36, 1029 (2003) · Zbl 1066.81007 · doi:10.1088/0305-4470/36/4/312 |
| [27] | Fernandez, F.M., Guardiola, R., Ros, J., Znojil, M.: J. Phys. A 32, 3105 (1999) · Zbl 0943.34075 · doi:10.1088/0305-4470/32/17/303 |
| [28] | de Dutra, S.A.: Phys. Lett. A 339, 252 (2005) · Zbl 1145.81364 · doi:10.1016/j.physleta.2005.02.075 |
| [29] | Weigert, S.: Phys. Rev. A 68, 062111 (2003) · doi:10.1103/PhysRevA.68.062111 |
| [30] | Bender, C.M., Cooper, F., Meisinger, P.N.: Phys. Lett. A 259, 229 (1999) · Zbl 0948.81536 · doi:10.1016/S0375-9601(99)00468-5 |
| [31] | Buslaev, V., Grecchi, V.: J. Phys. A 36, 5541 (1993) · Zbl 0817.47077 · doi:10.1088/0305-4470/26/20/035 |
| [32] | Delabaere, E., Bham, F.: Phys. Lett. A 250, 25 (1998) · doi:10.1016/S0375-9601(98)00791-9 |
| [33] | Bender, C.M., Milton, K.A., Savage, V.M.: Phys. Rev. D 62, 085001 (2000) · doi:10.1103/PhysRevD.62.085001 |
| [34] | Bender, C.M., Boettcher, S., Jones, H.F., Meisinger, P.N.: J. Math. Phys. 42, 1960 (2001) · Zbl 1015.81048 · doi:10.1063/1.1361063 |
| [35] | Znojil, M.: J. Phys. A 36, 7639 (2003) · Zbl 1052.81104 · doi:10.1088/0305-4470/36/27/315 |
| [36] | Znojil, M.: J. Phys. A 36, 7825 (2003) · Zbl 1029.81020 · doi:10.1088/0305-4470/36/28/311 |
| [37] | Yesiltas, O., Simsek, M., Sever, R., Tezcan, C.: Phys. Scr. T 67, 472 (2003) · Zbl 1045.35060 · doi:10.1238/Physica.Regular.067a00472 |
| [38] | Taseli, H.: J. Phys. A 31, 779 (1998) · Zbl 0956.81011 · doi:10.1088/0305-4470/31/2/032 |
| [39] | Znojil, M.: Phys. Lett. A 264, 108 (1999) · Zbl 0949.81020 · doi:10.1016/S0375-9601(99)00805-1 |
| [40] | Levai, G., Znojil, M.: J. Phys. A 35, 8793 (2002) · Zbl 1044.81578 · doi:10.1088/0305-4470/35/41/311 |
| [41] | Faridfathi, G., Sever, R., Aktas, M.: J. Math. Chem. 38, 533 (2005) · Zbl 1100.81028 · doi:10.1007/s10910-005-6900-8 |
| [42] | Aktas, M., Sever, R.: Mod. Phys. Lett. A 19, 2871 (2004) · Zbl 1061.81030 · doi:10.1142/S0217732304015993 |
| [43] | Levai, G., Znojil, M.: J. Phys. A 33, 7165 (2000) · Zbl 0963.81012 · doi:10.1088/0305-4470/33/40/313 |
| [44] | Parthasarathi, Parashar, D., Kaushal, R.S.: J. Phys. A 37, 781 (2004) · Zbl 1074.81026 · doi:10.1088/0305-4470/37/3/017 |
| [45] | Dirac, P.A.M.: Rev. Mod. Phys. 17, 195 (1945) · Zbl 0060.45102 · doi:10.1103/RevModPhys.17.195 |
| [46] | Arai, A.: J. Math. Anal. Appl. 158, 63 (1991) · Zbl 0731.47055 · doi:10.1016/0022-247X(91)90267-4 |
| [47] | De, R., Dutt, R., Sukhatme, U.: J. Phys., A, Math. Gen. 25, L843 (1992) · doi:10.1088/0305-4470/25/13/013 |
| [48] | Buyukkilic, F., Egrifes, H., Demirhan, D.: Theor. Chim. Acta 98, 192 (1997) |
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.
