Solution of the Klein-Gordon Equation with PositionDependent Mass for Exponential Scalar and Vector Potentials by an Alternative Approach

Abstract

The s-wave Klein-Gordon equation, with position-dependent mass, is solved for the exponential vector and scalar potentials by an alternative approach. The asymptotic iteration method is used to obtain the energy eigenvalues. The results are the exact analytical and are in good agreement with the results previously.

Keywords

• Position-dependent mass
• Asymptotic Iteration Method (AIM)
• Klein-Gordon equation
• Exponential vector and scaler potentials
• Eigenvalues.

References

1. Arda, A., Sever, R., and Tezcan, C., “Analytical Solutions to the Klein–Gordon Equation with Position-Dependent Mass for q-Parameter Pöschl– Teller Potential”, Chin. Phys. Lett., 27: 010306 (2010).
2. Alhaidari, A. D., “Solution of the Dirac equation with position-dependent mass in the Coulomb field”, Phys. Lett. A, 322: 72-77 (2004).
3. Jia, C. S., Wang, P. Q., Liu, J. Y., and He, S., “Relativistic Confinement of Neutral Fermions with Partially Exactly Solvable and Exactly Solvable PT-Symmetric Potentials in the Presence of Position-Dependent Mass”, Int. J. Theor. Phys., 47: 2513-2522 (2008).
4. Arda, A., Sever, R., and Tezcan, C., “Approximate analytical solutions of the effective mass Dirac equation for the generalized Hulthén potential with any k-value”, Cent. Eur. J. Phys., 8: 843-849 (2010).
5. Mazharimousavi, S. H., Int. J. Theor. Phys., 47: 446 (2008).
6. Dai, T. Q., and Cheng, Y. Fu., “Bound state solutions withposition-dependent mass for the inversely linear potential”, Phys. Scr., 79: 015007 (2009).
7. Ikhdair, S. M., and Sever, R., “Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein–Gordon equation for the scalar and vector Hulthén potentials”, Phys. Scr., 79: 035002 (2009).
8. Arda, A., Sever, R., and Tezcan, C., “Approximate analytical solutions of the Klein–Gordon equation for the Hulthén potential with the position- dependent mass”, Phys. Scr., 79: 015006 (2009).

9. Serra, L., and Lipparini, E., “Spin response of unpolarized quantum dots”, Europhys. Lett., 40: 667 (1997).
10. Barranco, M., Pi, M., Gatica, S. M., Hernandez, E. S., and Navarro, “Structure and energetics of mixed 4He-3He drops”, J., Phys. Rev. B, 56: 8997 (1997).
11. Wanner, G. H., Phys. Rev., 52: 191 (1957).
12. Aygun, M., Bayrak, O., and Boztosun, I., “Solution of the radial Schrödinger equation for the potential family V (R) = A/r2 – B/r + Crk using the asymptotic iteration method”, J. Phys. B: At. Mol. Opt. Phys., 40: 537 (2007).
13. Aygun, M., Sahin, Y., and Boztosun, I., “Examination of V (R) = Z/r2 + gr + λr2 Potential in the presence of magnetic field”, Int. J. Mod. Phys. E, 19: 1349 (2010).
14. Bayrak, O., Boztosun, I., and Ciftci, H., “Exact Analytical Solutions to the Kratzer Potential by the Asymptotic Iteration Method”, Int. J. of Quantum Chemistry, 107: 540 (2007).
15. Soylu, A., Bayrak, O., and Boztosun, I., “Exact Solutions of Klein–Gordon Equation with Scalar and Chinese Phys. Lett., 25: 2754 (2008). Potentials”,
16. Durmus, A., and Yasuk, F., “Relativistic and nonrelativistic solutions for diatomic molecules in the presence of double ring-shaped Kratzer potential ”, J. Chem. Phys., 126: 074108 (2007).
17. Olğar, E., and Mutaf, H., “Asymptotic Iteration Method for Energies of Inversely Linear Potential with Spatially Dependent Mass”, Commun. Theor. Phys., 53: 1043-1045 (2010).
18. Olğar, E., Koç, R., and Tütüncüler, H., “The exact solution of the s-wave Klein–Gordon equation for the asymptotic iteration method”, Phys. Scr., 78: 015011 (2008). potential by the
19. Hamzavi, M., Rajabi, A. A., and Hassanabadi, H., “Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential interaction via asymptotic iteration method”, Phys. Lett. A 374, 4303-4307 (2010). tensor
20. Ciftci, H., Hall, R. L., and Saad, N., “Asymptotic iteration method for eigenvalue problems”, J. Phys. A: Math. Gen. 36, 11807 (2003).
21. Bayrak, O., and Boztosun, I., “Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method”, J. Phys. A: Math. Gen. 39, 6955 (2006).
22. Fernandez, F. M., “On an iteration method for eigenvalue problems”, J. Phys. A: Math. Gen. 37, 6173 (2004).
23. Chen, G., “Solution of the Klein–Gordon for exponential scalar and vector potentials”, Phys. Lett. A 339, 300-303 (2005).
24. Taskin, F., Boztosun, I., and Bayrak, O., “Exact Solutions Exponential Scalar and Vector Potentials”, Int. J. Theor. Phys. 47, 1612 (2008). Equation with
25. Dai, T. Q., “Bound state solutions of the s-wave Klein-Gordon equation with position dependent mass for exponential potential”, J. At. Mol. Sci. doi:
26. 4208/jams.012511.030511a (2011).