Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model
Applied and Computational Mathematics
Volume 6, Issue 1, February 2017, Pages: 54-59
Received: Nov. 23, 2016;
Accepted: Jan. 21, 2017;
Published: Feb. 24, 2017
Views 2650 Downloads 117
Akaninyene D. Antia, Department of Physics, Faculty of Science, University of Uyo, Uyo, Nigeria
Okon P. Akpan, Department of Science Technology, Akwa Ibom State Polytechnic, Ikot Ekpene, Nigeria
In this paper, we have solved the Schrödinger wave equation with Yukawa plus ring-shaped potential model using powerful Nikiforov-Uvarov method and obtained the energy eigenvalues and corresponding wave functions in terms of Jacobi and Laguerre polynomials for the angular and radial part respectively. We have also presented the effect of angle dependent solution on radial solutions and also applied our results to obtain numerical values for some selected diatomic molecules which suggest usefulness to other physical systems. We also studied the behavior of our potential graphically for H2 diatomic molecule.
Akaninyene D. Antia,
Okon P. Akpan,
Nonrelativistic Studies of Diatomic Molecules of Schrödinger Particles with Yukawa Plus Ring-Shaped Potential Model, Applied and Computational Mathematics.
Vol. 6, No. 1,
2017, pp. 54-59.
Zhang, X. A; Chen, K. and Duan, Z. L. (2005) Chinese physics.14, 42.
Dong, S. H; Sun, G. H. and Lozada-Cassou, M. (2005) Physical Letter. A328, 299.
Chen. C. Y. and Dong, S. H. (2005) Physical Letter. A335, 374.
Alhaidari, A. D. (2005) Solution of relativistic Dirac-Hulthen problems. Journal of Physics and Mathematics. Gen 38, 3409.
Zhang, M. C. and Wang, Z. B. (2005) Chinese Physical Letter. 22, 2994.
Roy, A. K. (2004) The generalized pseuduspectral approach to the bound state of the Hulthen and Yukawa potentials. Indian Journal of Physics. Vol. 65 No. 1 pp. 1-15.
Yukalov, V; Yukalova, E. and Oliveira, F. (1998). Renormaliziation group solutions for Yukawa potential. Journal of Physics. A31, 4337-4348.
Hamzavi, M; Movahedi, M; Thylwe, K-E and Rajabi, A. (2012) Approximate analytical solution of Yukawa Potential with arbituary angular momenta. Chinese Physics Letter. Vol. 29 No.8.
Hamzavi, M. and IKhdair, S. M. (2013) Relativistic symmetries of fermions in the background of inverse quadratic Yukawa potential as a tensor. Canadian Journal of Physics. A36, 11807-11818.
Ita, B; Ikot, A; Ikeuba, A. and Ebiekpe, V. (2014) Exact solution of Schrödinger equation for the Inverse quadratic Yukawa potential using Nikiforov-Uvarov method. Journal of Theoretical Physics and Cryptography. Vol. 5, pp.7-11.
Alhaidari, A; Bahlouli, H; Nasser, I; and Abdelmonem, M. (2008) an efficient mapped pseudospectral method for weakly bound state. Journal of Chemical Physics. A41, 032001.
IKhdair, S. M. and Sever, R. (2010) Approximate analytical solutions of the general Wood-Saxon potential including the Spin-orbit coupling term and spin symmetry. Central European Journal of Physics. Vol. 5, 2322-3138.
Antia, A. D; Umo, E. A. and Umoren, C. C. (2015) solution of nonrelativistic Schrödinger equation with Hulthen-Yukawa plus ange dependent potential within the framework of Nikiforov-Uvarov method. Journal of Theoretical Physics and Cryptography. Vol. 10, pp.1-8.
Yasuk, F; Durmus, A. and Boztosun, I. (2006) Exact analytical solution to the relativistic Klien-Gordon equation with a noncentral equal scalar and vector potentials. Journal of Mathematics and Physics. 49, 082302.
Hamzavi, M. and Rajabi, A. A. (2011) Exact solution of Dirac equation with Coulomb plus a novel angle dependent potential. Z. Naturforsch. 66a, 533.
Rajabi, A. A. and Hamzavi, M. (2013) A new coulomb ring shaped potential via generalized parametric Nikiforov-Uvarov method. Journal of Theoretical and Applied Physics. 7:17.
Zhang, M. C and Huang-Fu, G. Q. (2011) Pseudospin symmetry for a new oscillatory ring-shaped noncentral potential. Journal of Mathematics and Physics. 52, 053518.
Nikiforov, A. F. and Uvarov, V. B. (1988) Special Functions of Mathematical Physics. Basel: Birkhauser.
Tezcan, C. and Sever, R. (2009) A general approach of the exact solution of the Schrödinger equation. International Journal of Theoretical Physics. 48, 339.
Antia, A. D. and Ikot, A. N. (2014) Relativistic treatment of Spinless particles Subject to the Hulthen plus Yukawa potential with arbituary l-state. Advances in Physics Theory and Applications. Vol. 35, pp.27-35.
Landau, L. D. and Lifshitz, E. M. (1977) Quantum Mechanics. Non-Relativistic Theory. Canada: Pergamon.
Schiff, L. I. (1955) Quantum mechanics. New York: McGraw Hill.
Akcay, H. and Sever, R. (2011) Analytical solutions of schrodinger equation for the diatomic molecular potential with any angular potential. Journal of molecular Structure: Theochem. 845, 133.
Castro, E; Paz, J. and Martin, P. (2006) Journal of molecular Structure: Theochem. 46, 1122.
Khanna, K; Kanyeki, G; Rotich, S; Torongey, P. and Ameka, S. (2010) Anharmonic perturbation of neutron-proton pairs by the paired neutron in heavy finite nuclei. Indian Journal of Pure and Applied Physics. 48, 7-15.