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Chin. Phys. B, 2020, Vol. 29(9): 090301    DOI: 10.1088/1674-1056/ab928f
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Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials

Ruo-Lin Chai(柴若霖)1, Qiong-Tao Xie(谢琼涛)1, Xiao-Liang Liu(刘小良)2
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.
Keywords:  exact solutions      scattering states      non-Hermitian potential  
Received:  12 April 2020      Revised:  05 May 2020      Published:  05 September 2020
PACS:  03.65.Nk (Scattering theory)  
  02.30.Gp (Special functions)  
  42.82.Et (Waveguides, couplers, and arrays)  
Fund: Project supported by the Natural Science Foundation of Hainan Province, China (Grant No. 2019RC179).
Corresponding Authors:  Qiong-Tao Xie     E-mail:

Cite this article: 

Ruo-Lin Chai(柴若霖), Qiong-Tao Xie(谢琼涛), Xiao-Liang Liu(刘小良) Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials 2020 Chin. Phys. B 29 090301

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