  We investigate the static and dynamic properties of a Tonks-Girardeau gas in
a harmonic trap with an eccentric $\delta$-perturbation of variable strength.
For this we first find the analytic eigensolution of the single particle
problem and use this solution to calculate the spatial density and energy
profiles of the many particle gas as a function of the strength and position of
the perturbation. We find that the crystal nature of the Tonks state is
reflected in both the lowest occupation number and momentum distribution of the
gas. As a novel application of our model, we study the time evolution of the
the spatial density after a sudden removal of the perturbation. The dynamics
exhibits collapses and revivals of the original density distribution which
occur in units of the trap frequency. This is reminiscent of the Talbot effect
from classical optics.
