Exactly solvable complex PT symmetry potential $A[\mathrm{sech}({\lambda}x) + i\tanh({\lambda}x)]$

TL;DR

This paper presents exact solutions for a novel complex PT-symmetric potential, revealing the absence of bound states and exploring the effects of handedness and phase factors in transmission.

Contribution

It introduces a new exactly solvable PT-symmetric potential and analyzes its unique scattering properties, including the handedness effect and phase shifts.

Findings

No bound states in the potential

Handedness effect observed in reflection coefficients

Transmission phase factors depend on incident direction

Abstract

We obtained the exactly solutions of the $\mathcal{PT}$ symmetric potential $V(x)=A[\sech(\lambda x)+i \tanh(\lambda x)]$, and found this system has no bound-state. which $\mathcal{PT}$ symmetric potential was first studied in this article, and the handedness effect is showed from reflection coefficients. As the asymptotically non-vanishing imaginary potential component, when the direction of the incident wave is opposite, that the transmission coefficient will emerge a complex phase factor.