Arbitrary l-state solutions of the Schrödinger equation for the Eckart potential with an improved approximation of the centrifugal term

• Authors: Jerzy Stanek
• Languages of publication: EN

Abstracts

EN

Applying an improved approximation scheme to the centrifugal term, the approximate analytical solutions of the Schrödinger equation for the Eckart potential are presented. Bound state energy eigenvalues and the corresponding eigenfunctions are obtained in closed forms for the arbitrary radial and angular momentum quantum numbers, and different values of the screening parameter. The results are compared with those obtained by the other approximate and numerical methods. It is shown that the present method is systematic, more efficient and accurate.

Keywords

EN

bound states; Eckart potential; centrifugal term

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2011
• Volume: 9
• Issue: 6
• Pages: 1503-1508

Dates

published

1 - 12 - 2011

online

15 - 10 - 2011

Contributors

author

Jerzy Stanek

• Faculty of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60-780, Poznań, Poland

References

• [1] C. L. Pekeris, Phys. Rev. 45, 98 (1934) http://dx.doi.org/10.1103/PhysRev.45.98[Crossref]
• [2] R. L. Greene, C. Aldrich, Phys. Rev. A 14, 2363 (1976) http://dx.doi.org/10.1103/PhysRevA.14.2363[Crossref]
• [3] M. Badawi, N. Bessis, G. Bessis, Journal of Physics B: Atomic and Molecular Physics 5, L157 (1972) http://dx.doi.org/10.1088/0022-3700/5/8/004[Crossref]
• [4] J. Lu, Phys. Scripta 72, 349 (2005) http://dx.doi.org/10.1238/Physica.Regular.072a00349[Crossref]
• [5] S. M. Ikhdair, R. Sever, Ann. Phys-Berlin 18, 189 (2009) http://dx.doi.org/10.1002/andp.200810349[Crossref]
• [6] C. S. Jia, J. Y. Liu, P. Q. Wang, Phys. Lett. A 372, 4779 (2008) http://dx.doi.org/10.1016/j.physleta.2008.05.030[Crossref]
• [7] S. M. Ikhdair, R. Sever, arXiv:0807.2085v1 [quant-ph]
• [8] S. H. Dong, W. C. Qiang, G. H. Sun, V. B. Bezerra, J. Phys. A-Math. Theor. 40, 10535 (2007) http://dx.doi.org/10.1088/1751-8113/40/34/010[Crossref]
• [9] A. P. Zhang, W. C. Qiang, Y. W. Ling, Chinese Phys. Lett. 26, 100302 (2009) http://dx.doi.org/10.1088/0256-307X/26/10/100302[Crossref]
• [10] C. Y. Chen, D. S. Sun, F. L. Lu, J. Phys. A-Math. Theor. 41, 035302 (2008) http://dx.doi.org/10.1088/1751-8113/41/3/035302[Crossref]
• [11] X. Y. Liu, G. F. Wei, C. Y. Long, Int. J. Theor. Phys. 48, 463 (2009) http://dx.doi.org/10.1007/s10773-008-9821-z[Crossref]
• [12] F. Taşkin, G. Koąk, Chinese Phys. B 19, 090314 (2010) http://dx.doi.org/10.1088/1674-1056/19/9/090314[Crossref]
• [13] C. Eckart, Phys. Rev. 35, 1303 (1930) http://dx.doi.org/10.1103/PhysRev.35.1303[Crossref]
• [14] I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series, and Products, 7th edition (Academic Press, New York, 2007)
• [15] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, New York, 1972)
• [16] W. Lucha, F. F. Schöberl, Int. J. Mod. Phys. C 10, 607 (1999) http://dx.doi.org/10.1142/S0129183199000450[Crossref]
• [17] D. A. Morales, Chem. Phys. Lett. 394, 68 (2004) http://dx.doi.org/10.1016/j.cplett.2004.06.109[Crossref]

Identifiers

DOI

10.2478/s11534-011-0071-y