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## Path Integral Solution of PT-/non-PT-Symmetric and non-Hermitian Hulthen Potential

N. Kandirmaz, R. Sever

The wave functions and the energy spectrum of PT-/non-PT-Symmetric and non-Hermitian Hulthen potential are of an exponential type and are obtained via the path integral. The path integral is constructed using parametric time and point transformation.

Scattering from a discrete quasi-Hermitian delta function potential is studied and the metric operator is found. A generalized continuity relation in the physical Hilbert space $${\mathcal H}_{{\rm phys}}$$ is derived and the probability current density is defined. The reflection $${\mathcal R}$$ and transmission $${\mathcal T}$$ coefficients computed with this current are shown to obey the unitarity relation $${\mathcal R}+{\mathcal T}=1$$.