Exactly solvable complex PT symmetry potential A[sech(λx) + i tanh(λx)]

Abstract

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