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A stochastic model of a continuous nondemolition observation of a quantum system is presented. The nonlinear stochastic wave equation describing the posterior dynamics of the observed quantum system is solved for a free particle of mass m>0. It is shown that the dispersion of the Gaussian wave packet does not increase to infinity as for a free unobserved particle, but tends to the finite limit τ_∞²=({}/2{λ}m)1/2, where {λ} is the accuracy coefficient of an indirect nondemolition measurement of the particle's position.
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Belavkin et al. (1992) studied this question.
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