Abstract
The irreversible and stochastic behaviour of the continuously (in time) observed quantum system expressed by the reduction of the wave function cannot be described within the standard formulation of quantum mechanics. The state of a quantum system under continuous nondemolition observation evolves according to weakly-nonlinear filtering equation announced by Belavkin in 1988. This quantum stochastic differential equation of Ito type can be obtained from the unitary evolution of the compound system — “system plus measuring device” by conditioning with respect to the measuring trajectories. The equation has been applied to some significant physical problems. These include: stochastic resolution of quantum Zeno paradox for a free particle, watchdog effects for quantum particle for various cases of the diffusion nondemolition measurement and relaxation without mixing of an atom under a counting observation.
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