  We explore a way of finding the link between a non-Hermitian Hamiltonian and
a Hermitian one. Based on the analysis of Bethe Ansatz solutions for a class of
non-Hermitian Hamiltonians and the scattering problems for the corresponding
Hermitian Hamiltonians. It is shown that a scattering state of an arbitrary
Hermitian lattice embedded in a chain as the scattering center shares the same
wave function with the corresponding non-Hermitian tight binding lattice, which
consists of the Hermitian lattice with two additional on-site complex
potentials, no matter the non-Hermitian is broken PT symmetry or even non-PT.
An exactly solvable model is presented to demonstrate the main points of this
article.
