N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation

Year 2018, , 97 - 103, 29.06.2018

Hasan Fatih Kisoglu

https://doi.org/10.17350/HJSE19030000079

Abstract

The energy eigenvalues and eigenfunctions of relativistic scalar particles are obtained for an equal vector and scalar symmetrical molecular potential in N-dimensional euclidean space by using Asymptotic Iteration Method. For such a calculation, the potential in the eigenvalue equation is scaled regarding to fact that the potential is the same in non-relativistic limit. Furthermore, an highly-accurate approximation scheme is used to deal with the centrifugal term in the eigenvalue equation. The results obtained are compared with the ones that exist in literature.

Keywords

Klein-Gordon equation, Asymptotic Iteration Method, Symmetrical molecular potential, Centrifugal term

References

• 1. Greiner, W. Relativistic Quantum Mechanics, third ed. Springer, Berlin, 2000.
• 2. Landau, L. D., Lifshitz, E. M. Quantum Mechanics NonRelativistic Theory, second ed. Pergamon, London, 1965.
• 3. Buyukkilic, F., Egrifes, H., Demirhan, D. Solution of the Schrödinger equation for two different molecular potentials by the Nikiforov-Uvarov method. Theor. Chem. Acc. 98 (1997) 192-196.
• 4. Yang, Q. B. Deformed Symmetrical Double-well Potential. Acta. Photon. Sin. 32 (2003) 882-884.
• 5. Arai, A. Exactly solvable supersymmetric quantum mechanics. J. Math. Anal. Appl. 158 (1991) 63-79.
• 6. Zhao, X. Q., Jia, C. S., Yang, Q. B. Bound states of relativistic particles in the generalized symmetrical double-well potential. Phys. Lett. A 337 (2005) 189-196.
• 7. Wei, G. F., Chen, W. L. Arbitrary l-wave bound states of the Schrödinger equation for the hyperbolical molecular potential. Int. J. Quantum Chem. 114 (2014), 1602-1606.
• 8. Wei, G. F., Chen, W. L., Dong, S. H. The arbitrary l continuum states of the hyperbolic molecular potential. Phys. Lett. A 378 (2014) 2367-2370.
• 9. Candemir, N. Klein–Gordon particles in symmetrical well potential. Appl. Math. Comput. 274 (2016) 531–538.
• 10. Nikiforov, A.F., Uvarov, V.B. Special functions of mathematical physics: a unified introduction with applications, first ed. Birkhäuser, 1988.
• 11. Greene, R.L., Aldrich, C. Variational wave functions for a screened Coulomb potential. Phys. Rev. A 14 (1976) 2363– 2366.
• 12. Ciftci, H., Hall, R.L., Saad, N. Asymptotic iteration method for eigenvalue problems. J. Phys. A: Math. Gen. 36 (2003) 11807–11816.
• 13. Ciftci, H., Hall, R.L., Saad, N. Perturbation theory in a framework of iteration methods. Phys. Lett. A 340 (2005) 388–396.
• 14. Ciftci, H., Hall, R.L., Saad, N. Exact and approximate solutions of Schrödinger's equation for a class of trigonometric potentials. Centr. Eur. J. Phys. 11 (2013) 37–48.
• 15. Ikhdair, S.M. An improved approximation scheme for the centrifugal term and the Hulthén potential. Eur. Phys. J. A 39 (2009) 307–314.
• 16. Aydogdu, O., Yanar, H. Bound and scattering states for a hyperbolic-type potential in view of a new developed approximation. Int. J. Quantum Chem. 115 (2015) 529–534.
• 17. Alhaidari, A.D., Bahlouli, H., Al-Hasan, A. Dirac and Klein– Gordon equations with equal scalar and vector potentials. Phys. Lett. A 349 (2006) 87–97.
• 18. Yasuk, F., Durmus, A., Boztosun, I. Exact analytical solution to the relativistic Klein–Gordon equation with noncentral equal scalar and vector potentials. J. Math. Phys. 47 (2006) 082302.
• 19. Ciftci, H., Hall, R.L., Saad, N. Construction of exact solutions to eigenvalue problems by the asymptotic iteration method. J. Phys. A: Math. Gen. 38 (2005) 1147–1156.
• 20. Ol ar, E., Koç, R., Tütüncüler, H. The exact solution of the s-wave Klein–Gordon equation for the generalized Hulthén potential by the asymptotic iteration method. Phys. Scr. 78 (2008) 015011.
• 21. Alsadi, K.S. Exact Solutions of Dirac-Rosen-Morse Problem via Asymptotic Iteration Method. J. Nanoelectron. Optoe. 10 (2015) 683–687.
• 22. Hall, R.L., Saad, N. Schrödinger spectrum generated by the Cornell potential. Open Phys. 13 (2015) 83–89.
• 23. Fernandez, F.M. On an iteration method for eigenvalue problems. J. Phys. A: Math. Gen. 37 (2004) 6173–6180.
• 24. Barakat, T., Al-Dossary, O.M. The Asymptotic Iteration Method For The Eigenenergies Of The Asymmetrical Quantum Anharmonic Oscillator Potentials. Int. J. Mod. Phys. A 22 (2007) 203–212.
• 25. Nieto, M. M. Hydrogen atom and relativistic pi–mesic atom in N-space dimensions. Am. J. Phys. 47 (1979) 1067–1072.
• 26. Avery, J. Hyperspherical Harmonics: Applications in Quantum Theory, first ed. Kluwer Academic Publishers, 1989.
• 27. Cavalli, S., Aquilanti, V., Grossi, G. Hyperspherical coordinates for molecular dynamics by the method of trees and the mapping of potential energy surfaces for triatomic systems. J. Chem. Phys. 85 (1986) 1362–1375.
• 28. Nouri, S. Generalized coherent states for the d-dimensional Coulomb problem. Phys. Rev. A 60 (1999) 1702–1705.
• 29. Avery, J. Hyperspherical Harmonics and Generalized Sturmians, first ed. Kluwer Academic Publishers, 2002.
• 30. Diaz, R., Pariguan, E. On hypergeometric functions and Pochhammer k-symbol. Divulg. Mat. 15 (2007) 179–192.
• 31. Mubeen, S., Rehman, A. A Note on k-Gamma Function and Pochhammer k-Symbol. Journal of Informatics and Mathematical Sciences 6 (2014) 93–107.
• 32. Ciftci, H., Kisoglu, H.F. Application of asymptotic iteration method to a deformed well problem. Chinese Phys. B 25 (2016) 030201.
• 33. Kisoglu, H.F., Ciftci, H. Accidental Degeneracies in N dimensions for Potential Class via Asymptotic Iteration Method (AIM). Commun. Theor. Phys. 67 (2017) 350–354.
• 34. Kiriushcheva, N., Kuzmin, S. Scattering of a Gaussian wave packet by a reflectionless potential. Am. J. Phys 66 (1998) 867–872.
• 35. Qiang, W.-C. Bound states of the Klein–Gordon and Dirac equations for potential . Chin. Phys. 13 (2004) 571.