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BOUND-STATES OF A SEMI-RELATIVISTIC EQUATION FOR THE -SYMMETRIC GENERALIZED HULTHÉN POTENTIAL BY THE NIKIFOROV–UVAROV METHOD

SAMEER M. IKHDAIR

Department of Physics, Near East University, Nicosia, TRNC, Mersin 10, Turkey

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and

RAMAZAN SEVER

Department of Physics, Middle East Technical University, 06531 Ankara, Turkey

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https://doi.org/10.1142/S0218301308010337Cited by:33 (Source: Crossref)

Abstract

The one-dimensional semi-relativistic equation has been solved for the -symmetric generalized Hulthén potential. The Nikiforov–Uvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type, is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthén potentials.

Keywords:

PACS: 03.65.-w, 03.65.Fd, 03.65.Ge

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References

C. M. Bender, G. V. Dunne and P. N. Meisenger, Phys. Lett. A 252, 272 (1999), DOI: 10.1016/S0375-9601(98)00960-8. Crossref, Web of Science, ADS, Google Scholar
G. S. Japaridze, J. Phys. A: Math. Gen. 35, 1709 (2002), DOI: 10.1088/0305-4470/35/7/315. Crossref, ADS, Google Scholar
A. Khare and B. P. Mandal, Phys. Lett. A 272, 53 (2000), DOI: 10.1016/S0375-9601(00)00409-6. Crossref, Web of Science, ADS, Google Scholar
F. Cannata, G. Junker and J. Trost, Phys. Lett. A 246, 219 (1998), DOI: 10.1016/S0375-9601(98)00517-9. Crossref, Web of Science, ADS, Google Scholar
B. Bagchi and C. Quesne, Phys. Lett. A 273 (2000) 285; B. Bagchi and C. Quesne, Phys. Lett. A 300 (2002) 18 . Google Scholar
Z. Ahmad, Phys. Lett. A 273, 343 (2000). Google Scholar
A. Mostafazadeh, J. Math. Phys. 43, 3944 (2002), DOI: 10.1063/1.1489072. Crossref, Web of Science, ADS, Google Scholar
M. Znojil, Phys. Lett. A 264, 108 (1999), DOI: 10.1016/S0375-9601(99)00805-1. Crossref, Web of Science, ADS, Google Scholar
C. M. Bender, M. Berry, P. N. Meisenger, V. M. Savage and M. Simsek, J. Phys. A: Math. Gen. 34 (2001) L31; C. M. Bender, S. Boettcher, H. F. Jones, P. N. Meisenger and M. Simsek, Phys. Lett. A 291 (2001) 197 . Google Scholar
R. N. Deb, A. Khare and B. D. Roy, Phys. Lett. A 307, 215 (2003). Web of Science, Google Scholar
N. Hatano and D. R. Nelson, Phys. Rev. B 56, 8651 (1997), DOI: 10.1103/PhysRevB.56.8651. Crossref, Web of Science, ADS, Google Scholar
D. R. Nelson and N. M. Shnerb, Phys. Rev. E 58, 1383 (1998), DOI: 10.1103/PhysRevE.58.1383. Crossref, Web of Science, ADS, Google Scholar
C. M. Bender, D. C. Brody and H. F. Jones, Phys. Rev. Lett. 89, 27 (2002), DOI: 10.1103/PhysRevLett.89.270401. Google Scholar
N. N. Bogolubov , A. A. Logunov and I. I. Todorov , Introduction to Axiomatic Field Theory ( Benjamin , New York , 1975 ) . Google Scholar
G. Barton, Ann. Phys. 166, 322 (1986). Crossref, Web of Science, ADS, Google Scholar
S. Flügge , Practical Quantum Mechanics I ( Springer-Verlag , Berlin , 1974 ) . Google Scholar
L. D. Landau and E. M. Lifshitz , Quantum Mechanics ( Pergamon Press , London , 1958 ) . Google Scholar
P. M. Morse and H. Feshbach , Methods of Theoretical Physics ( McGraw-Hill , New York , 1953 ) . Google Scholar
B. Sahu, S. K. Agarwalla and C. S. Shastry, J. Phys. A: Math. Gen. 35, 4349 (2002), DOI: 10.1088/0305-4470/35/19/314. Crossref, ADS, Google Scholar
A. Khare and U. P. Sukhatme, J. Phys. A: Math. Gen. 21, L501 (1988), DOI: 10.1088/0305-4470/21/9/005. Crossref, Google Scholar
Z. Ahmed, Phys. Lett. A 157, 1 (1991), DOI: 10.1016/0375-9601(91)90399-S. Crossref, Web of Science, ADS, Google Scholar
Z. Ahmed, Phys. Rev. A 47, 4757 (1993), DOI: 10.1103/PhysRevA.47.4761. Google Scholar
M. Znojil, Phys. Lett. A 264, 108 (1999), DOI: 10.1016/S0375-9601(99)00805-1. Crossref, Web of Science, ADS, Google Scholar
D. T. Barclayet al., Phys. Lett. A 305, 231 (2002). Web of Science, Google Scholar
G. Lévai and M. Znojil, J. Phys. A: math. Gen. 35, 8793 (2002), DOI: 10.1088/0305-4470/35/41/311. Crossref, Google Scholar
C. S. Jia, X. L. Zeng and L. T. Sun, Phys. Lett. A 294, 185 (2002), DOI: 10.1016/S0375-9601(01)00840-4. Crossref, Web of Science, ADS, Google Scholar
Z. Ahmed, Phys. Lett. A 290, 19 (2001), DOI: 10.1016/S0375-9601(01)00622-3. Crossref, Web of Science, ADS, Google Scholar
C. M. Bender and S. Boettcher, J. Phys. A 31, 1273 (1998), DOI: 10.1088/0305-4470/31/14/001. Google Scholar
M. Znojil, J. Phys. A: Math. Gen. 33, 4203 (2000), DOI: 10.1088/0305-4470/33/22/320. Crossref, ADS, Google Scholar
F. Yasuket al., Phys. Scr. 71, 340 (2005). Crossref, Web of Science, ADS, Google Scholar
M. Simsek and H. Egrifes, J. Phys. A: Math. Gen. 37, 4379 (2004), DOI: 10.1088/0305-4470/37/15/007. Crossref, ADS, Google Scholar
H. Egrifes and R. Sever, Phys. Lett. A 344, 117 (2005), DOI: 10.1016/j.physleta.2005.06.061. Crossref, Web of Science, ADS, Google Scholar
S. M. Ikhdair and R. Sever, Hadronic J. 15 (1992) 389; Int. J. Mod. Phys. A 18 (2003) 4215; Int. J. Mod. Phys. A 20 (2005) 4035; Int. J. Mod. Phys. A 21 (2006) 2191; Int. J. Mod. Phys. A 21 (2006) 3989; Int. J. Mod. Phys. A 21 (2006) 6699; Int. J. Mod. Phys. E 17 (2008) 669; Int. J. Mod. Phys. A 19 (2004) 1771; S. Ikhdair et al., Tr. J. Phys. 16 (1992) 510; Tr. J. Phys. 17 (1993) 474 . Google Scholar
S. M. Ikhdair and R. Sever, Z. Phys. D 28 (1993) 1; J. Math. Chem. 41 (2007) 329; J. Math. Chem. 41 (2007) 343; Int. J. Mod. Phys. A 21 (2006) 6465; J. Mol. Struct: Theochem 809 (2007) 103; J. Mol. Struct: Theochem 806 (2007) 155; J. Mol. Struct: Theochem 855 (2008) 13; Centr. Eur. J. Phys. 5 (2007) 516; Centr. Eur. J. Phys. 6 (2008) 141; Int. J. Mod. Phys. C 19 (2008) 221; S. M. Ikhdair, Chin. J. Phys 46 (2008) 291 . Google Scholar
M. Znojil, J. Phys. A: Math. Gen. 14, 383 (1981), DOI: 10.1088/0305-4470/14/2/015. Crossref, ADS, Google Scholar
F. Dominguez-Adame, Phys. Lett. A 136, 175 (1989). Crossref, Web of Science, ADS, Google Scholar
L. Chetouaniet al., Physica A 234, 529 (1996), DOI: 10.1016/S0378-4371(96)00288-9. Crossref, Web of Science, ADS, Google Scholar
N. A. Rao and B. A. Kagali, Phys. Lett. A 296 (2002) 192; S. M. Ikhdair and R. Sever, to appear in the Cent. E. J. Phys , arXiv: 0704.0573 . Google Scholar
M. Znojil, Phys. Lett. A 102, 289 (1984), DOI: 10.1016/0375-9601(84)90683-2. Crossref, Web of Science, ADS, Google Scholar
S. M. Ikhdair and R. Sever, Ann. Phys. (Berlin) 16, 218 (2007), DOI: 10.1002/andp.200610232. Crossref, Web of Science, ADS, Google Scholar
S. M. Ikhdair and R. Sever, Int. J. Theor. Phys. 46 (2007) 1643; Int. J. Theor. Phys. 46 (2007) 2384; C. Berkdemir, A. Berkdemir and R. Sever, Phys. Rev. C 72 (2005) 027001 . Google Scholar
A. F. Nikiforov and V. B. Uvarov , Special Functions of Mathematical Physics ( Birkhauser , Basel , 1988 ) . Crossref, Google Scholar
E. E. Salpeter and H. A. Bethe, Phys. Rev. 84 (1951) 1232; E. E. Salpeter, Phys. Rev. 87 (1952) 328 . Google Scholar
G. Jaczko and L. Durand, Phys. Rev. D 58, 114017 (1998), DOI: 10.1103/PhysRevD.58.114017. Crossref, Web of Science, ADS, Google Scholar
S. M. Ikhdair and R. Sever, Z. Phys. C 56 (1992) 155; S. M. Ikhdair and R. Sever, Z. Phys. C 58 (1993) 153 . Google Scholar
S. M. Ikhdair and R. Sever, Int. J. Mod. Phys. A 19 (2004) 1771; Int. J. Mod. Phys. A 20 (2005) 6509 . Google Scholar
W. Lucha, F. F. Schöberl and D. Gromes, Phys. Rep. 200, 127 (1991), DOI: 10.1016/0370-1573(91)90001-3. Crossref, Web of Science, ADS, Google Scholar
M. R. Arafahet al., Ann. Phys. 220, 55 (1992). Crossref, Web of Science, ADS, Google Scholar
C. Olsonet al., Phys. Rev. D 45, 4307 (1992), DOI: 10.1103/PhysRevD.45.4307. Crossref, Web of Science, ADS, Google Scholar
B. Durand and L. Durand, Phys. Rev. D 25 (1982) 2312; B. Durand and L. Durand, Phys. Rev. D 30 (1984) 1904; J. Nickisch, L. Durand and B. Durand, Phys. Rev. D. 30 (1984) 660 . Google Scholar
L. Hulthén, Ark. Mat. Astron. Fys. A 28, 5 (1942). Google Scholar
S. M. Ikhdair and R. Sever, J. Math. Chem. 42 (2007) 461; B. Gönül and İ Zorba, Phys. Lett. A 269 (2000) 83 . Google Scholar
W. Magnus , F. Oberhettinger and R. P. Soni , Formulas and Theorems for the Special Function of Mathematical Physics , 3rd edn. ( Springer , Berlin , 1966 ) . Crossref, Google Scholar
A. P. Prudrinkov , Yu. A. Brychkov and O. I. Marichev , Integrals and Series ( Gordon and Breach , New York , 1986 ) . Google Scholar
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Dover, New York) p. 1964. Google Scholar
B. Bagchi, C. Quesne and M. Znojil, Mod. Phys. Lett. A 16, 2047 (2001). Link, Web of Science, Google Scholar
C. S. Jia, P. Y. Lin and L. T. Sun, Phys. Lett. A 298, 78 (2002), DOI: 10.1016/S0375-9601(02)00467-X. Crossref, Web of Science, ADS, Google Scholar