Scattering theory for the Belavkin equation describing a quantum particle with continuously observed coordinate

In the paper, the complete investigation is given of the large times behavior of solutions of the Belavkin quantum filtering equation describing a quantum particle with continuously observed coordinate. It turns out, in particular, that these solutions have extraordinary property that can be interpreted as a sort of confinement. Namely, as t→∞, any linear combination of Gaussian wave packets will tends to a single one for almost all realizations of innovating Wiener process. In other words, several initial particles will stick together at large times, i.e. they can not be identified in the process of measurement. As a consequence, it follows that the dispersion of coordinate will always tend to the same limit, as t→∞, not depending on initial data. (orig.)