1 College of Physics and Electronic Engineering, Hainan Normal University, Haikou 571158, China; 2 School of Physics and Electronics, Central South University, Changsha 410083, China
Abstract The scattering states in one-dimensional Hermitian and non-Hermitian potentials are investigated. An analytical solution for the scattering states is presented in terms of Heun functions. It is shown that for some specially chosen parameter conditions, an infinite number of the exact scattering states is obtained. In the Hermitian potentials, they correspond to the reflectionless states. In the non-Hermitian complex potentials with parity-time symmetry, they are the unidirectionally reflectionless states.
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