Research PapersNo Access

ANALYTICAL SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE MANNING–ROSEN POTENTIAL PLUS A RING-SHAPED-LIKE POTENTIAL

Department of Mathematical Physics, Faculty of Applied Mathematics and Cybernetics, Baku State University, Z. Khalilov St. 23, AZ-1148, Baku, Azerbaijan

Search for more papers by this author

C. AYDIN

Department of Physics, Karadeniz Technical University, 61080, Trabzon, Turkey

Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK

Search for more papers by this author

N. SH. HUSEYNOVA

Institute of Applied Mathematics Baku State University, Z. Khalilov St. 23, AZ-1148, Baku, Azerbaijan

Search for more papers by this author

, and

O. UZUN

Department of Physics, Karadeniz Technical University, 61080, Trabzon, Turkey

Search for more papers by this author

https://doi.org/10.1142/S0218301313500729Cited by:23 (Source: Crossref)

Abstract

The analytical solution of the Schrödinger equation for the Manning–Rosen potential plus a ring-shaped-like potential is obtained by applying the Nikiforov–Uvarov method by using the improved approximation scheme to the centrifugal potential for arbitrary l states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary l states.

Keywords:

PACS: 03.65.Ge

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

W. Greiner, Quantum Mechanics, 4th edn. (Springer, Berlin, 2001). Crossref, Google Scholar
V. G. Bagrov and D. M. Gitman , Exact Solutions of Relativistic Wave Equations ( Kluwer Academic Publishers , Dordrecht , 1990 ) . Crossref, Google Scholar
S. Flügge , Practical Quantum Mechanics 1 ( Springer , Berlin , 1994 ) . Google Scholar
M. F. Manning , Phys. Rev. 44 , 951 ( 1933 ) . Crossref, Google Scholar
M. F. Manning and N. Rosen , Phys. Rev. 44 , 953 ( 1933 ) . Google Scholar
S.-H. Dong and J. Garcia-Ravelo , Phys. Scripta 75 , 307 ( 2007 ) . Crossref, Web of Science, ADS, Google Scholar
W.-C. Qiang and S.-H. Dong , Phys. Lett. A 368 , 13 ( 2007 ) . Crossref, Web of Science, ADS, Google Scholar
A. A. Makarov et al. , Nuovo Cimento A 52 , 1061 ( 1967 ) . Crossref, Web of Science, ADS, Google Scholar
F. Cooper , A. Khare and U. Sukhatme , Phys. Rep. 251 , 267 ( 1995 ) . Crossref, Web of Science, ADS, Google Scholar
D. A. Morales , Chem. Phys. Lett. 394 , 68 ( 2004 ) . Crossref, Web of Science, ADS, Google Scholar
S.-H. Dong , Factorization Method in Quantum Mechanics ( Springer , Dordrecht , 2007 ) . Crossref, Google Scholar
A. Arda and R. Sever , Commun. Theor. Phys. 58 , 27 ( 2012 ) . Crossref, Web of Science, ADS, Google Scholar
J. Cai , P. Cai and A. Inomata , Phys. Rev. A 34 , 4621 ( 1986 ) . Crossref, Web of Science, ADS, Google Scholar
A. F. Nikiforov and V. B. Uvarov , Special Functions of Mathematical Physics ( Birkhäuser , Basel , 1988 ) . Crossref, Google Scholar
V. H. Badalov , H. I. Ahmadov and A. I. Ahmadov , Int. J. Mod. Phys. E 18 , 631 ( 2009 ) . Link, ADS, Google Scholar
V. H. Badalov , H. I. Ahmadov and S. V. Badalov , Int. J. Mod. Phys. E 19 , 1463 ( 2010 ) . Link, Web of Science, ADS, Google Scholar
V. H. Badalov and H. I. Ahmadov, , arXiv:math-ph/1111.4734 . Google Scholar
Y. P. Varshni , Phys. Rev. A 41 , 4682 ( 1990 ) . Crossref, Web of Science, ADS, Google Scholar
A. D. Antia , A. N. Ikot and L. E. Akpabio , Eur. J. Sci. Res. 46 , 107 ( 2010 ) . Google Scholar
C. S. Jia , T. Chen and L. G. Cui , Phys. Lett. A 373 , 1621 ( 2009 ) . Crossref, Web of Science, ADS, Google Scholar
R. L. Greene and C. Aldrich , Phys. Rev. A 14 , 2363 ( 1976 ) . Crossref, Web of Science, ADS, Google Scholar
I. Area et al. , J. Comput. Appl. Math. 157 , 93 ( 2003 ) . Crossref, Web of Science, ADS, Google Scholar
M. Abramowitz and I. A. Stegun , Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables ( Dover , New York , 1964 ) . Google Scholar
D. Agboola , Commun. Theor. Phys. 55 , 972 ( 2011 ) . Crossref, Web of Science, ADS, Google Scholar
Z.-Y. Chen , M. Li and C.-S. Jia , Mod. Phys. Lett. A 24 , 1863 ( 2009 ) . Link, Web of Science, ADS, Google Scholar