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

Abstract

We obtained the exactly solutions of the $\mathcal{P}\mathcal{T}$ symmetric potential $V(x)=A[\sech(λx)+i \tanh(λx)]$, and found this system has no bound-state. which $\mathcal{P}\mathcal{T}$ 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.