  Given the abstract wave equation $\ddot\phi-\Delta_\alpha\phi=0$, where
$\Delta_\alpha$ is the Laplace operator with a point interaction of strength
$\alpha$, we define and study $\bar W_\alpha$, the associated wave generator in
the phase space of finite energy states. We prove the existence of the phase
flow generated by $\bar W_\alpha$, and describe its most relevant properties
with particular emphasis on the associated symplectic structure and scattering
theory
