Abstract
We have obtained analytically the bound state solutions for the non-relativistic Schrodinger equation for the Eckart plus inversely quadratic Yukawa potential (EIQYP) using the parametric Nikiforov-Uvarov (NU) method. In order to validate our approximation, the bound state energies were computed and predicted for some selected diatomic molecules at different adjustable screening parameters from the available spectroscopic model parameters. The fact-finding obtained are in agreement with previously reported results available in literature. Furthermore, the graphs of the effective potential against inter-nuclear distance for low and high values of the screening parameters were reported. From our graphs, we observed that the approximation is best fit for very low values of the screening parameter α ≪ 1.
Similar content being viewed by others
References
Onate CA, Onyeaju MC, Ikot AN, Idiodi JOA, Ojonubah JO (2017) Eigen solutions, Shannon entropy and fisher information under the Eckart Manning Rosen potential model. Journal of the Korean Physical Society 70(4):339–347
Sari RA, Suparmi A, Cari C (2015) Solution of Dirac equation for Eckart potential and trigonometric manning Rosen potential using asymptotic iteration method. Chinese Physics B 25(1):010301
Greene RL, Aldrich C (1976) Variational wave functions for a screened Coulomb potential. Phys. Rev. A 14(6):2363
Chen CY, Sun DS, Lu FL (2008) Analytical approximations of scattering states to the l-wave solutions for the Schrödinger equation with the Eckart potential. J. Phys. A Math. Theor. 41(3):035302
Ikhdair SM Bound states of the Klein-Gordon equation in D-dimensions with some physical scalar and vector exponential-type potentials including orbital centrifugal term. arXiv preprint arXiv:1110.0943 (2011)
Hassanabadi H, Yazarloo BH, Zarrinkamar S (2013) Exact solution of Klein–Gordon equation for Hua plus modified Eckart potentials. Few-Body Systems 54(11):2017–2025
Zhang Y (2008) Approximate analytical solutions of the Klein–Gordon equation with scalar and vector Eckart potentials. Phys. Scr. 78(1):015006
Taskin F, Koçak GÖKHAN (2010) Approximate solutions of Schrödinger equation for Eckart potential with centrifugal term. Chinese Physics B 19(9):090314
Akpan IO, Antia AD, Ikot AN (2012) Bound-state solutions of the Klein-Gordon equation with-deformed equal scalar and vector Eckart potential using a newly improved approximation scheme. ISRN High Energy Physics
Qiang WC, Dong SH (2007) Arbitrary l-state solutions of the rotating Morse potential through the exact quantization rule method. Phys. Lett. A 363(3):169–176
Suparmi A, Cari C, Handhika J (2013) Approximate solution of Schrodinger equation for Eckart potential combined with Trigonormetric Poschl-teller non-central potential using Romanovski polynomials. Journal of Physics: Conference Series 423(1):012039
Hamzavi M, Ikhdair SM, Ita BI (2012) Approximate spin and pseudospin solutions to the Dirac equation for the inversely quadratic Yukawa potential and tensor interaction. Phys. Scr. 85(4):045009
Ita BI, Louis H, Magu TO, Nzeata-Ibe NA (2017) Bound state solutions of the Schrӧdinger’s equation with Manning-Rosen plus a class of Yukawa potential using Pekeris-like approximation of the Coulomb term and parametric Nikiforov-Uvarov. World Scientific News 70(2):312–319
Louis, B. I. Ita, PI Amos, OU Akakuru, MM Orosun, NA Nzeata-Ibe and M. Philip bound state solutions of Klein-Gordon equation with Manning-Rosen plus a class of Yukawa potential using pekeris-like approximation of the Coulomb term and parametric Nikiforov-Uvarov. International Journal of Chemical and Physical Sciences, 7(1), (2018) 33–37
Onate CA, Ojonubah JO (2016) Eigensolutions of the Schrödinger equation with a class of Yukawa potentials via supersymmetric approach. Journal of Theoretical and Applied Physics 10(1):21–26
Maireche A (2017) Effects of two-dimensional noncommutative theories on bound states Schrödinger diatomic molecules under new modified Kratzer-type interactions. International Letters of Chemistry, Physics and Astronomy 76:1–11
Hamzavi M, Thylwe KE, Rajabi AA (2013) Approximate bound states solution of the Hellmann potential. Commun. Theor. Phys. 60(1):1
Edet CO, Okorie US, Osobonye G, Ikot AN, Rampho GJ, Sever R (2020) Thermal properties of Deng–Fan–Eckart potential model using Poisson summation approach. J. Math. Chem.:1–25
Ramazan, Sever, Cevdet, Teczan, Metin, Aktas, Ozlem, Yesiltas. (2018). Exact solution of Schrodinger equation for Pseudoharmonic potential. arXiv:quant-ph/0701206v1
Oyewumi KJ, Sen KD (2012) Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules. J. Math. Chem. 50(5):1039–1059
Acknowledgments
Mr. Philemon is thankful to Professor Benedict Ita for his general contributions which led to the success of this research work.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ita, B.I., Louis, H., Ubana, E.I. et al. Evaluation of the bound state energies of some diatomic molecules from the approximate solutions of the Schrodinger equation with Eckart plus inversely quadratic Yukawa potential. J Mol Model 26, 349 (2020). https://doi.org/10.1007/s00894-020-04593-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00894-020-04593-0