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

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

DOI: 10.17350/HJSE19030000079

Full Text: page_white_acrobat.png

Downloads

Download data is not yet available.

References

1. Greiner, W. Relativistic Quantum Mechanics, third ed. Springer, Berlin, 2000.

2. Landau, L. D., Lifshitz, E. M. Quantum Mechanics Non- Relativistic 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. Olar, 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.
Published
2018-04-06
How to Cite
Kisoglu, H. F. (2018). N-Dimensional Solutions of Klein-Gordon Particles for Scaled Molecular Potential via Highly-Accurate Approximation. Hittite Journal of Science & Engineering, 5(2), 97-103. Retrieved from https://www.hjse.hitit.edu.tr/hjse/index.php/HJSE/article/view/HJSE19030000079
Section
SCIENCE