  We explore an alternative way of finding the link between a PT non-Hermitian
Hamiltonian and a Hermitian one. Based on the analysis of the scattering
problem for an imaginary potential and its time reversal process, it is shown
that any real-energy eigenstate of a PT tight-binding lattice with on-site
imaginary potentials shares the same wave function with a resonant transmission
state of the corresponding Hermitian lattice embedded in a chain. It indicates
that the PT eigenstate of a PT non-Hermitian Hamiltonian has connection to the
resonance transmission state of the extended Hermitian Hamiltonian.
