Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access April 23, 2014

Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

Eser Olğar EMAIL logo , Hayder Dhahir and Haydar Mutaf
From the journal Open Physics

Abstract

The bound state solution of Coulomb Potential in the Dirac equation is calculated for a position dependent mass function M(r) within the framework of the asymptotic iteration method (AIM). The eigenfunctions are derived in terms of hypergeometric function and function generator equations of AIM.

[1] W. Greiner, Relativistic Quantum Mechanics Wave Equation, 3rd edition (Freankfert, Germen, 1987) Search in Google Scholar

[2] A. D. Saavedra, F. Boronat, J. Polls, A. Fabrocini, Phys. Rev. B 50, 4248 (1994) http://dx.doi.org/10.1103/PhysRevB.50.424810.1103/PhysRevB.50.4248Search in Google Scholar

[3] T. Gora, F. Williams, Phys. Rev. 177, 1179 (1969) http://dx.doi.org/10.1103/PhysRev.177.117910.1103/PhysRev.177.1179Search in Google Scholar

[4] A. D. Alhaidari, Phys. Rev. A 75, 042707 (2007) http://dx.doi.org/10.1103/PhysRevA.75.04270710.1103/PhysRevA.75.042707Search in Google Scholar

[5] A. D. Alhaidari, H. Bahlouli, A. Al Hasan, M. S. Abdelmonem, Phys. Rev. A 75, 062711 (2007) http://dx.doi.org/10.1103/PhysRevA.75.06271110.1103/PhysRevA.75.062711Search in Google Scholar

[6] A. D. Alhaidari, Phys. Lett. A 322, 72 (2004) http://dx.doi.org/10.1016/j.physleta.2004.01.00610.1016/j.physleta.2004.01.006Search in Google Scholar

[7] O. Panella, S. Biondini, A. Arda, J. Phys. A Math. Theor. 43, 325302 (2010) http://dx.doi.org/10.1088/1751-8113/43/32/32530210.1088/1751-8113/43/32/325302Search in Google Scholar

[8] A. De Souza Dutra, C. S. Jia, Phys. Lett. 352, 484 (2010) http://dx.doi.org/10.1016/j.physleta.2005.12.04810.1016/j.physleta.2005.12.048Search in Google Scholar

[9] I. O. Vakarchuk, J. Phy. A Math. Gen. 38, 4727 (2005) http://dx.doi.org/10.1088/0305-4470/38/21/01610.1088/0305-4470/38/21/016Search in Google Scholar

[10] S. M. Ikhadair, R. Sever, Appl. Math. Comput. 216, 911 (2010) http://dx.doi.org/10.1016/j.amc.2010.01.10410.1016/j.amc.2010.01.104Search in Google Scholar

[11] C. S. Jia, T. Chen, L. G. Cui, Phys. Lett. A 373, 1621 (2009) http://dx.doi.org/10.1016/j.physleta.2009.03.00610.1016/j.physleta.2009.03.006Search in Google Scholar

[12] C. S. Jia, A. de Souza Dutra, Ann. Phys. 323, 566 (2008) http://dx.doi.org/10.1016/j.aop.2007.04.00710.1016/j.aop.2007.04.007Search in Google Scholar

[13] L. Dekar, L. Chetouani, T. F. Hammann, J. Math. Phys. 39, 2551 (1998) http://dx.doi.org/10.1063/1.53240710.1063/1.532407Search in Google Scholar

[14] X. L. Peng, J. Y. Liu, C. S. Jia, Phys. Lett. A 352, 478 (2006) http://dx.doi.org/10.1016/j.physleta.2005.12.03910.1016/j.physleta.2005.12.039Search in Google Scholar

[15] D. Agboola, math-ph/arxiv:1011, 2368v1 Search in Google Scholar

[16] J. Yu, S. H. Dong, G. H. Sun, Phys. Lett. A 322, 290 (2004) http://dx.doi.org/10.1016/j.physleta.2004.01.03910.1016/j.physleta.2004.01.039Search in Google Scholar

[17] J. Yu, S. H. Dong, Phys. Lett. A 325, 194 (2004) http://dx.doi.org/10.1016/j.physleta.2004.03.05610.1016/j.physleta.2004.03.056Search in Google Scholar

[18] S. H. Dong, J. J. Pena, C. P. Garcia, J. G. Ravelo, Mod. Phys. Lett. A 22, 1039 (2007) http://dx.doi.org/10.1142/S021773230702147010.1142/S0217732307021470Search in Google Scholar

[19] J. Wu., Y. Alhassid, J. Math. Phys. 31, 557 (1990) http://dx.doi.org/10.1063/1.52888910.1063/1.528889Search in Google Scholar

[20] R. A. Swainson, G. W. F. Drake, J. Phys. A: Math. Gen. 24, 79 (1991) http://dx.doi.org/10.1088/0305-4470/24/1/01910.1088/0305-4470/24/1/019Search in Google Scholar

[21] G. Chen, Phys. Lett. A 326, 55 (2004) http://dx.doi.org/10.1016/j.physleta.2004.04.02910.1016/j.physleta.2004.04.029Search in Google Scholar

[22] L. Infeld, T. E. Hull, Rev. Mod. Phys. 23, 21 (1951) http://dx.doi.org/10.1103/RevModPhys.23.2110.1103/RevModPhys.23.21Search in Google Scholar

[23] R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals, (McGraw-Hill, New York, 1965) Search in Google Scholar

[24] C. Grosche, J. Phys. A. Math. Gen. 28, 5889 (1995) http://dx.doi.org/10.1088/0305-4470/28/20/01810.1088/0305-4470/28/20/018Search in Google Scholar

[25] E. Witten, Nucl. Phys. B 188, 513 (1981) http://dx.doi.org/10.1016/0550-3213(81)90006-710.1016/0550-3213(81)90006-7Search in Google Scholar

[26] A. Comtet, A. Bandrank, D. K. Campbell, Phys. Lett. B 150, 159 (1985) http://dx.doi.org/10.1016/0370-2693(85)90160-110.1016/0370-2693(85)90160-1Search in Google Scholar

[27] S. H. Dong, X. Y. Gu, Z. Q. Ma, S. Dong, Int. J. Mod. Phys. E. 11, 483 (2002) http://dx.doi.org/10.1142/S021830130200104610.1142/S0218301302001046Search in Google Scholar

[28] S. H. Dong, G. H. Sun, D. Popov, J. Math. Phys. 44, 4467 (2003) http://dx.doi.org/10.1063/1.160418510.1063/1.1604185Search in Google Scholar

[29] S. H. Dong, M. L. Cassou, Phys. Lett. A 330, 168 (2004) http://dx.doi.org/10.1016/j.physleta.2004.08.00810.1016/j.physleta.2004.08.008Search in Google Scholar

[30] G. de A. Marques, V. B. Bezerra, S. H. Dong, Mod. Phys. Lett. A 28, 1350137 (2013) http://dx.doi.org/10.1142/S021773231350137X10.1142/S021773231350137XSearch in Google Scholar

[31] H. Ciftci, R. L. Hall, N. Saad, J. Phys. A: Math. Gen. 36, 11807 (2003) http://dx.doi.org/10.1088/0305-4470/36/47/00810.1088/0305-4470/36/47/008Search in Google Scholar

[32] H. Ciftci, R. L. Hall, N. Saad, J. Phys. A: Math. Gen. 38, 1147 (2005) http://dx.doi.org/10.1088/0305-4470/38/5/01510.1088/0305-4470/38/5/015Search in Google Scholar

[33] F. M. Fernandez, J. Phys. A. Math. Gen. 37, 617332 (2004) http://dx.doi.org/10.1088/0305-4470/37/23/01410.1088/0305-4470/37/23/014Search in Google Scholar

[34] T. Barakat, K. Abodayeh, A. Mukheimer, J. Phys. A. Math. Gen. 38, 1299 (2005) http://dx.doi.org/10.1088/0305-4470/38/6/00910.1088/0305-4470/38/6/009Search in Google Scholar

[35] T. Barakat, Phys. Lett. A 334, 411 (2005) http://dx.doi.org/10.1016/j.physleta.2005.06.08110.1016/j.physleta.2005.06.081Search in Google Scholar

[36] E. Olgar, R. Koç, H. Tütüncüler, Chin. Phys. Lett. 23, 539 (2006) http://dx.doi.org/10.1088/0256-307X/23/3/00410.1088/0256-307X/23/3/004Search in Google Scholar

[37] E. Olgar, Chin. Phys. Lett. 26, 020302 (2009) http://dx.doi.org/10.1088/0256-307X/26/2/02030210.1088/0256-307X/26/2/020302Search in Google Scholar

[38] E. Olgar, H. Mutaf, Commun. Theor. Phys. 53, 1043 (2010) http://dx.doi.org/10.1088/0253-6102/53/6/0910.1088/0253-6102/53/6/09Search in Google Scholar

[39] E. Olgar, Chin. Phys. Lett. 25, 1939 (2008) http://dx.doi.org/10.1088/0256-307X/25/6/00510.1088/0256-307X/25/6/005Search in Google Scholar

[40] E. Olgar, R. Koç, H. Tütüncüler, Phys. Scr. 78, 015011 (2008) http://dx.doi.org/10.1088/0031-8949/78/01/01501110.1088/0031-8949/78/01/015011Search in Google Scholar

[41] R. E. Moss, Am. J. Phys. 55, 397 (1987) http://dx.doi.org/10.1119/1.1514410.1119/1.15144Search in Google Scholar

[42] H. Galic, Am. J. Phys. 56, 312 (1988) http://dx.doi.org/10.1119/1.1563010.1119/1.15630Search in Google Scholar

[43] S. H. Dong, Z. Q. Ma., Phys. Lett. 312, 78 (2003) http://dx.doi.org/10.1016/S0375-9601(03)00606-610.1016/S0375-9601(03)00606-6Search in Google Scholar

[44] D. Agboola, Int. J. Quantum Chem. 112, 1029 (2012) http://dx.doi.org/10.1002/qua.2309010.1002/qua.23090Search in Google Scholar

[45] D. Agboola, Few Body Syst. 52, 31 (2012) http://dx.doi.org/10.1007/s00601-011-0235-810.1007/s00601-011-0235-8Search in Google Scholar

[46] D. Agboola, Pramana. Phys. 76, 875 (2011) http://dx.doi.org/10.1007/s12043-011-0104-510.1007/s12043-011-0104-5Search in Google Scholar

[47] G. Esposito, P. Santorelli, J. Phys. A. Gen. 32, 5643 (1999) http://dx.doi.org/10.1088/0305-4470/32/30/31010.1088/0305-4470/32/30/310Search in Google Scholar

[48] M. Hamzavi, A. A. Rajabi, H. Hassanabadi, Phys. Lett. A 374, 4303 (2010) http://dx.doi.org/10.1016/j.physleta.2010.08.06510.1016/j.physleta.2010.08.065Search in Google Scholar

[49] S. M. Ikhdair, R. Sever, Appl. Math. Phys. 316, 545 (2010) 10.1016/j.amc.2010.01.072Search in Google Scholar

Published Online: 2014-4-23
Published in Print: 2014-4-1

© 2014 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 9.12.2022 from https://www.degruyter.com/document/doi/10.2478/s11534-014-0448-9/html
Scroll Up Arrow