Exact Polynomial Solution of 𝒫𝒯-/Non-𝒫𝒯-Symmetric and Non-Hermitian Modified Woods–Saxon Potential by the Nikiforov–Uvarov Method

Using the Nikiforov–Uvarov (NU) method, the bound state energy eigenvalues and eigenfunctions of the 𝒫𝒯-/non-𝒫𝒯-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 𝒫𝒯-symmetric quantum mechanics, we exactly solved the time-independent Schrödinger 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.