Exact Polynomial Solution of $${\cal P}{\cal T}$/Non-${\cal P}{\cal T}$$- Symmetric and Non-Hermitian Modified Woods–Saxon Potential by the Nikiforov–Uvarov Method

Abstract

Using the Nikiforov–Uvarov (NU) method, the bound state energy eigenvalues and eigenfunctions of the $${\cal P{\cal T}}$-/non-${\cal P}{\cal T}$$ -symmetric and non-Hermitian modified Woods–Saxon (WS) model potential with the real and complex-valued energy levels are obtained in terms of the Jacobi polynomials. According to the $${\cal P}{\cal T}$$ -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.