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arXiv:quant-ph/0410152

Exact Supersymmetric Solution of PT Non PT Symmetric and non Hermitian Generalized Woods Saxon Potential

Cüneyt Berkdemir, Ayşe Berkdemir, R. Sever

Published Oct 20, 2004• 2 citations
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Abstract

Exact Supersymmetric solution of Schrodinger equation is obtained for PT non PT symmetric and non Hermitian generalized Woods Saxon potential to get the real and complex valued energy eigenvalues and the corresponding eigenfunctions for the bound states. Nikiforov Uvarov method is used in the calculations.

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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.