  The balance of gain and loss in an open system may maintain certain Hermitian
dynamical behaviors, which can be hardly observed in a popular Hermitian
system. In this paper, we systematically study a 1D PT -symmetry non-Hermitian
SSH model with open boundary condition based on exact approximate solution. We
show that the long-wave length standing-wave modes can be achieved within the
linear dispersion region when the system is tuned at the exceptional point
(EP). The whole Hilbert space can be decomposed into two quasi-Hermitian
subspaces, which are consisted of positive and negative energy levels,
respectively. Within each subspace, the system maintains all the features of a
Hermitian one. We construct a coherent-like state in a subspace and find that
it exhibits perfect simple harmonic motion (SHM). In contrast to a canonical
coherent state, the shape of the wavepacket deforms periodically rather than
entirely translation. And the amplitude of the SHM is not determined by the
initial condition but the shape of the wavepacket. Our result indicates that
novel Hermitian dynamics can be realized by a non-Hermitian system.
