  We show how the effective equation of motion for a distinguished quantum
particle in an ideal gas environment can be obtained by means of the monitoring
approach introduced in [EPL 77, 50007 (2007)]. The resulting Lindblad master
equation accounts for the quantum effects of the scattering dynamics in a
non-perturbative fashion and it describes decoherence and dissipation in a
unified framework. It incorporates various established equations as limiting
cases and reduces to the classical linear Boltzmann equation once the state is
diagonal in momentum.
