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arXiv:quant-ph/0610183 ¡ Annalen der Physik

Exact solution of the Klein-Gordon equation for the PT-symmetric generalized Woods-Saxon potential by the Nikiforov-Uvarov method

Sameer M. Ikhdair, R. Sever

Published Dec 21, 2006• 71 citations
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Abstract

The exact solution of the one-dimensional Klein-Gordon equation of the 𝒫𝒯-symmetric generalized Woods-Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s-states are also investigated for different types of complex generalized Woods-Saxon potentials.

DOI
10.1002/andp.200610232

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•Sep 21, 2011•0 citations
The exact solution of the one-dimensional Klein-Gordon equation of the 𝒫𝒯-symmetric generalized Woods-Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s-states are also investigated for different types of complex generalized Woods-Saxon potentials.
Using the Nikiforov-Uvarov method, the bound state energy eigenvalues and eigenfunctions of the PT-/non-PT-symmetric and non-Hermitian generalized Woods-Saxon (WS) potential with the real and complex-valued energy levels are obtained in terms of the Jacobi polynomials. According to the PT-symmetric quantum mechanics, we exactly solved the time-independent Schrodinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement with the ones obtained before.
Using the Nikiforov–Uvarov method which is based on solving the second-order differential equations, we firstly analyzed the energy spectra and eigenfunctions of the Woods–Saxon potential. In the framework of the PT-symmetric quantum mechanics, we secondly solved the time-independent Schrödinger equation for the PT and non-PT-symmetric version of the potential. It is shown that the discrete energy eigenvalues of the non-PT-symmetric potential consist of the real and imaginary parts, but the PT-symmetric one has a real spectrum. Results are obtained for s-states only.