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In this paper, we present a general method to solve non-hermetic potentialswith PT symmetry using the definition of two $\eta$-pseudo-hermetic andfirst-order operators. This generator applies to the Dirac equation whichconsists of two spinor wave functions and non-hermetic potentials, withposition that mass is considered a constant value and also Hamiltonianhierarchy method and the shape invariance property are used to performcalculations. Furthermore, we show the correlation between the potentialparameters with transmission probabilities that $\eta$-pseudo-hermetic usingthe change of focal points on Hamiltonian can be formalized based onSchr\"{o}dinger-like equation. By using this method for some solvablepotentials such as deformed Woods Saxon's potential, it can be shown that thesereal potentials can be decomposed into complex potentials consisting ofeigenvalues of a class of $\eta$-pseudo-hermitic.

The $\eta$-pseudo-hermitic generator in the deformed Woods Saxons potential