Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

• Authors: Hakan Ciftci , Richard Hall , Nasser Saad
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

trigonometric potentials; sine-squared potential; double-cosine potential; tangent-squared potential; cotangent complex potential; asymptotic iteration method; perturbation method

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 1
• Pages: 37-48

Dates

published

1 - 1 - 2013

online

15 - 1 - 2013

Contributors

author

Hakan Ciftci

• Gazi Üniversitesi, Fen-Edebiyat Fakültesi, Fizik Bölümü, Teknikokullar-Ankara, 06500, Turkey

author

Richard Hall

• Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montréal, Québec, H3G 1M8, Canada

author

Nasser Saad

• Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, PEI, C1A 4P3, Canada

References

• [1] T. Bakarat, J. Phys. A-Math. Gen. 39, 823 (2006) http://dx.doi.org/10.1088/0305-4470/39/4/007[Crossref]
• [2] H. Ciftci, R.L. Hall, N. Saad, J. Phys. A-Math. Gen. 36, 11807 (2003) http://dx.doi.org/10.1088/0305-4470/36/47/008[Crossref]
• [3] H. Ciftci, R.L. Hall, N. Saad, J. Phys. A-Math. Gen. 38, 1147 (2005) http://dx.doi.org/10.1088/0305-4470/38/5/015[Crossref]
• [4] B. Champion, R.L. Hall, N. Saad, Int. J. Mod. Phys. A 23, 1405 (2008) http://dx.doi.org/10.1142/S0217751X08039852[Crossref]
• [5] H. Ciftci, R.L. Hall, N. Saad, J. Phys. A-Math. Gen. 39, 2338 (2005)
• [6] H. Ciftci, R.L. Hall, N. Saad, Phys. Lett. A 340, 388 (2005) http://dx.doi.org/10.1016/j.physleta.2005.04.030[Crossref]
• [7] H. Ciftci, R.L. Hall, N. Saad, Phys. Rev. A 72, 022101 (2005)
• [8] C.B. Compean, M. Kirchbach, J. Phys. A-Math. Gen. 39, 547 (2006) http://dx.doi.org/10.1088/0305-4470/39/3/007[Crossref]
• [9] F. Gori, L. de la Torre, Eur. J. Phys. 24, 15 (2003) http://dx.doi.org/10.1088/0143-0807/24/1/301[Crossref]
• [10] K. Hai, W. Hai, Q. Chen, Phys. Lett. A 367, 445 (2007) http://dx.doi.org/10.1016/j.physleta.2007.03.042[Crossref]
• [11] M.M. Nieto, L.M. Simmons, Phys. Rev. D 20, 1332 (1979) http://dx.doi.org/10.1103/PhysRevD.20.1332[Crossref]
• [12] M.G. Marmorino, J. Math. Chem. 32, 303 (2002) http://dx.doi.org/10.1023/A:1022183225087[Crossref]
• [13] N.W. McLachlan, Theory and application of Mathieu functions (Dover, New York, 1964)
• [14] N. Saad, R.L. Hall, H. Ciftci, J. Phys. A-Math. Gen. 39, 13445 (2006) http://dx.doi.org/10.1088/0305-4470/39/43/004[Crossref]
• [15] H. Taseli, J. Math. Chem. 34, 243 (2003) http://dx.doi.org/10.1023/B:JOMC.0000004073.17023.41[Crossref]
• [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.2007.06.021[Crossref]
• [17] G.E. Andrews, R. Askey, R. Roy, Special Functions Encyclopedia of Mathematics and its Applications (Cambridge University Press, 2001)

Identifiers

DOI

10.2478/s11534-012-0147-3