There are two heavy particles (of mass $M$) and a light one (of mass $m<<M$). The light particles interact with heavy particle with an attracting dirac delta potential V=$-\delta(q-Q_1)-\delta(q-Q_2)$, where $q$ is the position of the light particle and $Q_1$ and $Q_2$ are the positions of the heavy particles.
It's claimed that because the heavy particles exchange light particles, a potential between the heavy particles arises. Why does this occur? How do I derive this?
I'm told to find it for short and large distances. It's all one-dimensional.