Spinless particles in the field of unequal scalar–vector Yukawa potentials

doi:10.1088/1674-1056/22/4/040301

Abstract We present analytical bound state solutions of the spin-zero Klein-Gordon (KG) particles in the field of unequal mixture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of Nikiforov-Uvarov (NU) method. Further, we solve the KG-Yukawa problem for its exact numerical energy eigenvalues via amplitude phase (AP) method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of KG-Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D=2-6.

Keywords: Klein-Gordon equation Yukawa potential D-dimensional space Nikiforov–Uvarov and amplitude phase methods

Received: 30 June 2012
Revised: 16 October 2012
Accepted manuscript online:

PACS:	03.65.Fd	(Algebraic methods)
	03.65.Pm	(Relativistic wave equations)
	03.65.Ca	(Formalism)
	03.65.Ge.

Corresponding Authors: M. Hamzavi, S. M. Ikhdair, K. E. Thylwe
E-mail: majid.hamzavi@gmail.com; sikhdair@neu.edu.tr, sikhdair@gmail.com; ket@mech.kth.se

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M. Hamzavi, S. M. Ikhdair, K. E. Thylwe Spinless particles in the field of unequal scalar–vector Yukawa potentials 2013 Chin. Phys. B 22 040301

[1]	Yukawa H 1935 Proc. Phys. Math. Soc. Jpn. 17 48
[2]	McEnnan J, Kissel L and Pratt R H 1976 Phys. Rev. A 13 532
[3]	Mehta C H and Patil S H 1978 Phys. Rev. A 17 34
[4]	Dutt R and Varshni Y P 1983 Z. Phys. A 313 143
[5]	Dutt R and Varshni Y P 1986 Z. Phys. D 2 207
[6]	Lai C S and Madan M P 1984 Z. Phys. A 316 131
[7]	Imbo T, Pagnamenta A and Sukhatme U 1984 Phys. Lett. A 105 183
[8]	Chakrabarti B and Das T K 2001 Phys. Lett. A 285 11
[9]	Ikhdair S M and Sever R 2006 Int. J. Mod. Phys. A 21 6465
[10]	Ikhdair S M and Sever R 2007 J. Mol. Struct.: Theochem 809 103
[11]	Zhang M C 2008 Chin. Phys. B 17 3214
[12]	Chargui Y, Chetouani L and Trabelsi A 2010 Chin. Phys. B 19 020305
[13]	Zhou Y and Guo J Y 2008 Chin. Phys. B 17 380
[14]	Zeng X X and Li Q 2009 Chin. Phys. B 18 4716
[15]	Xu J J, Ni G J and Lou S Y 2011 Chin. Phys. B 20 020302
[16]	Li H L 2011 Chin. Phys. B 20 030402
[17]	Taşkin F and Koçak G 2011 Chin. Phys. B 20 070302
[18]	Zhou S Q 2008 Chin. Phys. B 17 3812
[19]	Ma Z Y and Ma S H 2012 Chin. Phys. B 21 030507
[20]	Chen C Y, Lu F L and You Y 2012 Chin. Phys. B 21 030302
[21]	Hamzavi M, Eshghi M and Ikhdair S M 2012 J. Math. Phys. 53 082101
[22]	Lu F L and Chen C Y 2010 Chin. Phys. B 19 100309
[23]	Taskin F and Koçak G 2010 Chin. Phys. B 19 090314
[24]	Wei G F and Chen W L 2010 Chin. Phys. B 19 090308
[25]	Sun G H and Dong S H 2012 Commun. Theor. Phys. 58 195
[26]	Ikhdair S M and Hamzavi M 2012 Chin. Phys. B 21 110302
[27]	Kocak M and Gonül B 2007 Chin. Phys. Lett. 24 3024
[28]	Su K L 1997 Chin. Phys. Lett. 14 721
[29]	Long C Y, Qin S J, Zhang X and Wei G F 2008 Acta Phys. Sin. 57 6730 (in Chinese)
[30]	Wang Z B and Zhang M C 2007 Acta Phys. Sin. 56 3688 (in Chinese)
[31]	Zhang M C and Wang Z B 2006 Acta Phys. Sin. 55 525 (in Chinese)
[32]	Zhang M C and Wang Z B 2006 Acta Phys. Sin. 55 521 (in Chinese)
[33]	Lu F L and Chen C Y 2004 Acta Phys. Sin. 53 1652 (in Chinese)
[34]	Chen G 2004 Acta Phys. Sin. 53 684 (in Chinese)
[35]	Qiang W C 2002 Chin. Phys. 11 757
[36]	Li H M 2002 Chin. Phys. 11 1111
[37]	Fan H Y and Sun M Z 2001 Chin. Phys. 10 380
[38]	Li G L, Yue R H, Shi K J and Hou B Y 2001 Chin. Phys. 10 113
[39]	Lu H X, Zhang Y D and Wang X Q 2000 Chin. Phys. 9 325
[40]	Jing H and Wu J S 2000 Chin. Phys. 9 481
[41]	Chen C Y 2000 Chin. Phys. 9 731
[42]	Liu K J, Zhang Y D, Lu H X and Pan J W 2000 Chin. Phy. 9 5
[43]	Qiang W C 2003 Chin. Phys. 12 1054
[44]	Ni Z X 1999 Chin. Phys. 8 8
[45]	Dong S H 2011 Wave Equations in Higher Dimensions (Berlin: Springer-Verlag) pp. 181-202
[46]	Ikhdair S M 2011 J. Quantum Inf. Sci. 1 73
[47]	Nikiforov A F and Uvarov V B 1988 Special Functions of Mathematical Physics (Berlin: Birkhausr)
[48]	Ikhdair S M 2009 Int. J. Mod. Phys. C 20 25
[49]	Tezcan C and Sever R 2009 Int. J. Theor. Phys. 48 337
[50]	Korsch H J and Laurent H 1981 J. Phys. B: At. Mol. Phys. 14 4213
[51]	Yano T, Ezawa Y, Wada T and Ezawa H 2003 J. Comp. Appl. Math. 152 597
[52]	Thylwe K E 2004 J. Phys. A: Math. Gen. 37 L589
[53]	Thylwe K E 2009 Eur. Phys. J. D 54 591
[54]	Setare M R and Haidari S 2010 Phys. Scr. 81 065201
[55]	Aydoğdu O and Sever R 2011 Phys. Scr. 84 025005
[56]	Ikhdair S M 2012 Cent. Eur. J. Phys. 10 361
[57]	Hamzavi M, Ikhdair S M and Solaimani M 2012 Int. J. Mod. Phys. E 21 1250016
[58]	Hamzavi M, Movahedi M, Thylwe K E and Rajabi A A 2012 Chin. Phys. Lett. 29 080302
[59]	Karakoç M and Boztosun I 2006 Int. J. Mod. Phys. E 15 1253
[60]	Ikhdair S M and Sever R 2009 J. Math. Chem. 45 1137

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