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

doi:10.1088/1674-1056/ab928f

中国物理B ›› 2020, Vol. 29 ›› Issue (9): 90301-090301.doi: 10.1088/1674-1056/ab928f

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

Ruo-Lin Chai(柴若霖), Qiong-Tao Xie(谢琼涛), Xiao-Liang Liu(刘小良)

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

收稿日期:2020-04-12 修回日期:2020-05-05 接受日期:2020-05-13 出版日期:2020-09-05 发布日期:2020-09-05
通讯作者: Qiong-Tao Xie E-mail:qiongtaoxie@yahoo.com
基金资助:
Project supported by the Natural Science Foundation of Hainan Province, China (Grant No. 2019RC179).

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

Received:2020-04-12 Revised:2020-05-05 Accepted:2020-05-13 Online:2020-09-05 Published:2020-09-05
Contact: Qiong-Tao Xie E-mail:qiongtaoxie@yahoo.com
Supported by:
Project supported by the Natural Science Foundation of Hainan Province, China (Grant No. 2019RC179).

摘要/Abstract

摘要： 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.

关键词: exact solutions, scattering states, non-Hermitian potential

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.

Key words: exact solutions, scattering states, non-Hermitian potential

中图分类号: (Scattering theory)

03.65.Nk

02.30.Gp (Special functions) 42.82.Et (Waveguides, couplers, and arrays)

柴若霖, 谢琼涛, 刘小良. Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials[J]. 中国物理B, 2020, 29(9): 90301-090301.

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[J]. Chin. Phys. B, 2020, 29(9): 90301-090301.

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

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

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