  We prove a sharp dispersive estimate $$ |P_{ac}u(t,x)|\le
C|t|^{-1/2}\|u(0)\|_{L^1(R)} $$ for the one dimensional Schr\"odinger equation
$$ iu_{t}-u_{xx}+V(x)u+V_0 u=0, $$ where $(1+x^2)V\in L^1(R)$ and $V_0$ is a
step function, real valued and consant on the positive and negative real axes.
