Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials

doi:10.1088/1674-1056/ab928f

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
Accepted manuscript online: 13 May 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: qiongtaoxie@yahoo.com

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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Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials

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