Abstract
Two physically important potentials (Manning–Rosen and Pöschl-Teller) are considered for the ro-vibrational energy in diatomic molecules. An improved new approximation is invoked for the centrifugal term, which is then used for their solution within the Nikiforov–Uvarov framework. This employs a recently proposed scheme, which combines the two widely used Greene–Aldrich and Pekeris-type approximations. Thus, approximate analytical expressions are derived for eigenvalues and eigenfunctions. The energies are examined with respect to two approximation parameters, \(\lambda \) and \(\nu \). The original approximations are recovered for certain special values of these two parameters. This offers a simple effective scheme for these and other relevant potentials in quantum mechanics.
Similar content being viewed by others
References
M.F. Manning, N. Rosen, Phys. Rev. 44, 953 (1933)
A. Diaf, A. Chouchaoui, R.J. Lombard, Ann. Phys. 317, 354 (2005)
S.-H. Dong, J. García-Ravelo, Phys. Scr. 75, 307 (2007)
C.-Y. Chen, F.-L. Lu, D.-S. Sun, Phys. Scr. 76, 428 (2007)
W.-C. Qiang, S.-H. Dong, Phys. Lett. A 368, 13 (2007)
Z.-Y. Chen, M. Li, C.-S. Jia, Mod. Phys. Lett. A 24, 1863 (2009)
W.C. Qiang, S.-H. Dong, Phys. Scr. 79, 045004 (2009)
S.M. Ikhdair, Phys. Scr. 83, 015010 (2011)
A. Diaf, C. Chouchaoui, Phys. Scr. 84, 015004 (2011)
A. Abdel-Hady, in Proceedings of the 8th Conference on Nuclear and Particle Physics, NUPPAC-2011, Hurghada, Egypt (2011), p. 131
I. Nasser, M.S. Abdelmonem, A. Abdel-Hady, Mol. Phys. 111, 1 (2013)
W. Lucha, F.F. Schöberl, Int. J. Mod. Phys. C 10, 607 (1999)
A.K. Roy, Mod. Phys. Lett. A 29, 1450042 (2014)
X.-Y. Gu, S.-H. Dong, J. Math. Chem. 49, 2053 (2011)
G. Pöschl, E. Teller, Z. Phys. 83, 143 (1933)
S.H. Dong, W.C. Qiang, J. Garcóa-Ravelo, Int. J. Mod. Phys. A 23, 1537 (2008)
W.C. Qiang, S.-H. Dong, Int. J. Quantum Chem. 110, 2342 (2010)
H. Yanar, A. Tas, M. Salti, O. Aydogdu, Eur. Phys. J. Plus 135, 292 (2020)
R. Horchani, H. Jelassi, A.N. Ikot, U.S. Okorie, Int. J. Quantum Chem. 121, e26558 (2021)
W.C. Qiang, W.L. Chen, K. Li, G.F. Wei, Phys. Scr. 79, 025005 (2009)
Y. You, F.-L. Lu, D.-S. Sun, C.-Y. Chen, S.-H. Dong, Few-Body Syst. 54, 2125 (2013)
C.L. Pekeris, Phys. Rev. 45, 98 (1934)
M. Badawi, N. Bessis, G. Bessis, J. Phys. B 5, L157 (1972)
W.C. Qiang, J.Y. Wu, S.H. Dong, Phys. Scr. 79, 065011 (2009)
F.J.S. Ferreira, F.V. Prudente, Phys. Lett. A 377, 3027 (2013)
R.L. Greene, C. Aldrich, Phys. Rev. A 14, 2363 (1976)
D. Nath, A.K. Roy, Int. J. Quantum Chem. 121, e26616 (2021)
A.F. Nikiforov, V.B. Uvarov, Special Functions of Mathematical Physics (Birkhäuser, Basel, 1988)
G.F. Wei, C.Y. Long, S.H. Dong, Phys. Lett. A 372, 2592 (2008)
H.I. Ahmadov, C. Aydin, N.S.H. Huseynova, O. Uzun, Int. J. Mod. Phys. E 22, 1350072 (2013)
B.J. Falaye, K.J. Oyewumi, T.T. Ibrahim, M.A. Punyasena, C.A. Onate, Can. J. Phys. 91, 98 (2013)
W.C. Qiang, K. Li, W.L. Chen, J. Phys. A 42, 205306 (2009)
M.C. Onyeaju, J.O.A. Idiodi, A.N. Ikot, M. Solaimani, H. Hassanabadi, J. Opt. 46, 254 (2016)
H. Louis, B.I. Ita, N.I. Nzeata, Eur. Phys. J. Plus 134, 315 (2019)
B. Khirali, A.K. Behera, J. Bhoi, U. Laha, Ann. Phys. (NY) 412, 168044 (2020)
G.F. Wei, S.H. Dong, Phys. Lett. A 373, 49 (2008)
S.M. Ikhdair, R. Sever, Ann. Phys. (Berlin) 17, 897 (2008)
I.S. Gradshteyn, I.M. Ryzhik, Tables of Integals, Series, and Products, 5th edn. (Academic, New York, 1994)
A.K. Roy, Results Phys. 3, 103 (2013)
A.K. Roy, J. Math. Chem. 52, 1405 (2014)
Acknowledgements
AKR gratefully acknowledges financial support from MATRICS, DST-SERB, New Delhi (Sanction Order: MTR/2019/000012). We thank the anonymous referee for constructive comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nath, D., Roy, A.K. Ro-vibrational energy analysis of Manning–Rosen and Pöschl–Teller potentials with a new improved approximation in the centrifugal term. Eur. Phys. J. Plus 136, 430 (2021). https://doi.org/10.1140/epjp/s13360-021-01435-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-021-01435-7