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Inconsistencies are pointed out in the usual quantum versions of theclassical linear Boltzmann equation constructed for a quantized test particlein a gas. These are related to the incorrect formal treatment of momentumdecoherence. We prove that ideal collisions would result in complete momentumdecoherence, the persistence of coherence is only due to the finiteintercollision time. A corresponding novel quantum linear Boltzmann equation isproposed.

Quantum linear Boltzmann equation with finite intercollision time