The Asymptotic Iteration Method for the Eigenenergies of the a Novel Hyperbolic Single Wave Potential

Abdallah J.  Sous

doi:10.4236/jamp.2015.311168

Abdallah J. Sous

Abstract: By using the asymptotic iteration method, we have calculated numerically the eigenvalues En of the hyperbolic single wave potential which is introduced by H. Bahlouli, and A. D. Alhaidari. They found a new approach (the “potential parameter” approach) which has been adopted for this eigenvalues problem. For a fixed energy, the problem is solvable for a set of values of the potential parameters (the “parameter spectrum”). This paper will introduce a related work to complete the goal of finding the eigenvalues, the Schr?dinger equation with hyperbolic single wave potential is solved by using asymptotic iteration method. It is found that asymptotically this method gives accurate results for arbitrary parameters, V0, γ, and λ.

Keywords: Schrodinger Equation, Asymptotic Iteration Method, The Hyperbolic Single Wave Potential, Numerical Eigenenergies

Cite this paper: Sous, A. (2015) The Asymptotic Iteration Method for the Eigenenergies of the a Novel Hyperbolic Single Wave Potential. Journal of Applied Mathematics and Physics, 3, 1406-1411. doi: 10.4236/jamp.2015.311168.

References

[1] Alhaidari, G.A.D. (2007) Representation Reduction and Solution Space Contraction in Quasi-Exactly Solvable Systems. Journal of Physics A: Mathematical and Theoretical, 40, 6305-6328.
http://dx.doi.org/10.1088/1751-8113/40/24/004

[2] Asgarifar, S. and Goudarzi, H. (2013) Exact Solutions of the Manning-Rosen Potential Plus a Ring-Shaped Like Potential for the Dirac Equation: Spin and Pseudospin Symmetry. Physica Scripta, 87, 025703.
http://dx.doi.org/10.1088/0031-8949/87/02/025703

[3] Liu, K., Shi, W. and Wu, X.Y. (2013) An Extended Discrete Gradient Formula for Oscillatory Hamiltonian Systems. Journal of Physics A: Mathematical and Theoretical, 46, 165203.

[4] Moler, C.B. and Stewart, G.W. (1973) An Algorithm for Generalized Matrix Eigenvalue Problems. SIAM Journal on Numerical Analysis, 10, 241.
http://dx.doi.org/10.1137/0710024

[5] Suslov, S.K. (2010) Dynamical Invariants for Variable Quadratic Hamiltonians. Physica Scripta, 81, 055006.

[6] Pearman, C.M. (2014) An Excel-Based Implementation of the Spectral Method of Action Potential Alternans Analysis. Physiological Reports, 2, e12194.
http://dx.doi.org/10.14814/phy2.12194

[7] Roy, A.K. (2014) Studies on the Bound-State Spectrum of Hyperbolic Potential. Few-Body Systems, 55, 143-150.
http://dx.doi.org/10.1007/s00601-013-0767-1

[8] Bahlouli, H. and Alhaidari, A.D. (2010) Extending the Class of Solvable Potentials: III. The Hyperbolic Single Wave. Physica Scripta, 81, 025008.
http://dx.doi.org/10.1088/0031-8949/81/02/025008

[9] Alhaidari, A.D. and Bahlouli, H. (2009) Two New Solvable Potentials. Journal of Physics A: Mathematical and Theoretical, 42, No. 26.
http://dx.doi.org/10.1088/1751-8113/42/26/262001

[10] Ciftci, H., Hall, R.L. and Saad, N. (2003) Asymptotic Iteration Method for Eigenvalue Problems. Journal of Physics A: Mathematical and Theoretical, 36, 11807.
http://dx.doi.org/10.1088/0305-4470/36/47/008

[11] Ciftci, H., Hall, R.L. and Saad, N. (2005) Construction of Exact Solutions to Eigenvalue Problems by the Asymptotic Iteration Method. Journal of Physics A: Mathematical and General, 38, 1147-1155.
http://dx.doi.org/10.1088/0305-4470/38/5/015

[12] Saad, N., Hall, R.L. and Ciftci, H. (2006) Sextic Anharmonic Oscillators and Orthogonal Polynomials. Journal of Physics A: Mathematical and General, 39, 8477-8486.
http://dx.doi.org/10.1088/0305-4470/39/26/014

[13] Ozer, O. and Roy, P. (2009) The Asymptotic Iteration Method Applied to Certain Quasinormal Modes and Non Hermitian Systems. Central European Journal of Physics, 7, 747-752.

[14] Sous, A.J. (2006) Exact Solutions for a Hamiltonian Potential with Two-Parameters Using the Asymptotic Iteration Method. Chinese Journal of Physics, 44, 167-171.
http://psroc.phys.ntu.edu.tw/cjp/download.php?type=paper&vol=44&num=3&page=167

[15] Soylu, A., Bayrak, O. and Boztosun, I. (2007) An Approximate Solution of Dirac-Hulthén Problem with Pseudospin and Spin Symmetry for Any. Journal of Mathematical Physics, 48, 082302.
http://dx.doi.org/10.1063/1.2768436

[16] Barakat, T. (2005) The Asymptotic Iteration Method for the Eigenenergies of the Anharmonic Oscillator Potential . Physics Letters A, 344, 411-417.
http://dx.doi.org/10.1016/j.physleta.2005.06.081

[17] Sous, A.J. (2006) Solution for the Eigenenergies of the Sextic Anharmonic Oscillator . Modern Physics Letters A, 21, 1675.

[18] Sous, A.J. and EL-Kawni, M.I. (2009) General Eigenvalue Problems with Unbounded Potential from Below. International Journal of Modern Physics A, 24, 4169.
http://dx.doi.org/10.1142/s0217751x09044280