  A system of a particle and a harmonic oscillator, which have pure point
spectrum if uncoupled, is known to acquire absolutely continuous spectrum when
the particle and the oscillator are coupled by a sufficiently strong point
interaction. Here the simple dynamical mechanism underlying this phenomenon is
exposed. The energy of the oscillator is proven to exponentially diverge in
time, while the spatial probability distribution of the particle collapses into
a delta function in the interaction point. On account of this result, a
generalized model with many oscillators which interact with the particle at
different points is argued to provide a formal model for approximate
measurement of position, and collapse of wave packets.
