Does it make sense to define the mean free path in quantum mechanics? The mean free path defined in classical molecule dynamics has a strong classical flavor. Is it sensible to generalize the idea to quantum mechanics? 
 A: The mean free path can be meaningful quantity in quantum mechanics, although usually only in a semi-classical regime. It is particularly useful in the kinetic theory of quantum liquids at low temperature, where the excitations of the system can be described as quasiparticles that propagate approximately ballistically and interact only rarely.  You can define the mean free path as follows: let $\gamma$ be the rate of collisions between quasiparticles which have mean momentum $p$ and mass $m$; then the mean free path is $$l = \frac{p}{m\gamma}.$$ 
It is only really useful to describe the physics this way when the mean free path is much larger than the width of the quasiparticle's wave-packets (which is roughly related to their momentum). This leads to the approximate condition $l \gg \frac{\hbar}{p}$, or equivalently
$$ \frac{p^2}{2m} \gg \hbar \gamma.$$
In other words, the kinetic energy must dominate the energy scale of the quasiparticle interactions. Otherwise the system behaves in a collective fashion and it is not really appropriate to talk about independent quasiparticles.
These issues are discussed at length in Landau & Lifshitz Statistical Physics 2 and Physical Kinetics.
