Question 705052

A particle of energy $E$ is scattered off a one-dimensional potential $\lambda\delta(x)$, where $\lambda$ is a real positive constant, with a transmission amplitude $t_+$. In a different experiment, the same particle is scattered off another one-dimensional potential $-\lambda\delta(x)$, with a transmission amplitude $t_-$. In the limit $E \to 0$, the phase difference between $t_+$ and $t_-$ is