Solving the Deformed Woods–Saxon Potential with η -Pseudo-hermetic Generator

In this paper, we present a general method to solve the non-hermetic potentials with PT symmetry using the definition of two η-pseudo-hermetic and first-order operators. This generator applies to the Dirac equation which consists of two spinor wave functions and non-hermetic potential. Mass is considered a constant, and the Hamiltonian hierarchy method and the shape invariance property are used to perform calculations. Furthermore, we show the correlations between the potential parameters with transmission probabilities where η-pseudo-hermetic utilizing the change of focal points on Hamiltonian can be formalized based on Schrödinger-like equation. We employ this method for some solvable potentials such as deformed Woods–Saxon potential and show that these real potentials can be decomposed into complex potentials consisting of eigenvalues of a class of η-pseudo-hermetic generator.