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

摘要

Using the Nikiforov–Uvarov (NU) method, the bound state energy eigenvalues and eigenfunctions of the $${cal P{cal T}}$-on-${cal P}{cal T}$$ -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 Schr?dinger 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.