Nondemolition observation of a free quantum particle

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 ${\mathrm{\tau }}_{\mathrm{\infty }}^2$=(ħ/2λm${)}^{1/2}$, where λ is the accuracy coefficient of an indirect nondemolition measurement of the particle’s position.