Abstract
The asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using a coordinate transformation to reduce the Schrödinger equation to a second-order differential equation with an appropriate form. The asymptotic iteration method is also employed indirectly to obtain the terms in perturbation expansions, both for the energies and for the corresponding eigenfunctions.
[1] T. Bakarat, J. Phys. A-Math. Gen. 39, 823 (2006) http://dx.doi.org/10.1088/0305-4470/39/4/00710.1088/0305-4470/39/4/007Search in Google Scholar
[2] H. Ciftci, R.L. Hall, N. Saad, J. Phys. A-Math. Gen. 36, 11807 (2003) http://dx.doi.org/10.1088/0305-4470/36/47/00810.1088/0305-4470/36/47/008Search in Google Scholar
[3] H. Ciftci, R.L. Hall, N. Saad, J. Phys. A-Math. Gen. 38, 1147 (2005) http://dx.doi.org/10.1088/0305-4470/38/5/01510.1088/0305-4470/38/5/015Search in Google Scholar
[4] B. Champion, R.L. Hall, N. Saad, Int. J. Mod. Phys. A 23, 1405 (2008) http://dx.doi.org/10.1142/S0217751X0803985210.1142/S0217751X08039852Search in Google Scholar
[5] H. Ciftci, R.L. Hall, N. Saad, J. Phys. A-Math. Gen. 39, 2338 (2005) Search in Google Scholar
[6] H. Ciftci, R.L. Hall, N. Saad, Phys. Lett. A 340, 388 (2005) http://dx.doi.org/10.1016/j.physleta.2005.04.03010.1016/j.physleta.2005.04.030Search in Google Scholar
[7] H. Ciftci, R.L. Hall, N. Saad, Phys. Rev. A 72, 022101 (2005) 10.1103/PhysRevA.72.022101Search in Google Scholar
[8] C.B. Compean, M. Kirchbach, J. Phys. A-Math. Gen. 39, 547 (2006) http://dx.doi.org/10.1088/0305-4470/39/3/00710.1088/0305-4470/39/3/007Search in Google Scholar
[9] F. Gori, L. de la Torre, Eur. J. Phys. 24, 15 (2003) http://dx.doi.org/10.1088/0143-0807/24/1/30110.1088/0143-0807/24/1/301Search in Google Scholar
[10] K. Hai, W. Hai, Q. Chen, Phys. Lett. A 367, 445 (2007) http://dx.doi.org/10.1016/j.physleta.2007.03.04210.1016/j.physleta.2007.03.042Search in Google Scholar
[11] M.M. Nieto, L.M. Simmons, Phys. Rev. D 20, 1332 (1979) http://dx.doi.org/10.1103/PhysRevD.20.133210.1103/PhysRevD.20.1332Search in Google Scholar
[12] M.G. Marmorino, J. Math. Chem. 32, 303 (2002) http://dx.doi.org/10.1023/A:102218322508710.1023/A:1022183225087Search in Google Scholar
[13] N.W. McLachlan, Theory and application of Mathieu functions (Dover, New York, 1964) Search in Google Scholar
[14] N. Saad, R.L. Hall, H. Ciftci, J. Phys. A-Math. Gen. 39, 13445 (2006) http://dx.doi.org/10.1088/0305-4470/39/43/00410.1088/0305-4470/39/43/004Search in Google Scholar
[15] H. Taseli, J. Math. Chem. 34, 243 (2003) http://dx.doi.org/10.1023/B:JOMC.0000004073.17023.4110.1023/B:JOMC.0000004073.17023.41Search in Google Scholar
[16] Zhong-Qi Ma, A. Gonzalez-Cisneros, Bo-Wei Xu, Shi-Hai Dong, Phys. Lett. A 371, 180 (2007) http://dx.doi.org/10.1016/j.physleta.2007.06.02110.1016/j.physleta.2007.06.021Search in Google Scholar
[17] G.E. Andrews, R. Askey, R. Roy, Special Functions Encyclopedia of Mathematics and its Applications (Cambridge University Press, 2001) Search in Google Scholar
© 2012 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
