Consider an electron entering a grain of salt (NaCl). In a quantum mechanical description of the process the wavefunction of the electron will see more and more ions in its range of influence and so the relevant wave function will depend on more and more dynamical variables.
If one analyzes what this would mean in a computer simulation, only one conclusion is possible: the required storage space would grow exponentially with time and there would be now way to cope with a single grain of salt even if we had available as many supercomputers as there are Plancklength-sized cell in our earth.
So, the verbatim application of quantum mechanics on the motion of a charged particle after entering a ionic crystal is only possible if it is complemented by a reset and continue strategy. The inevitably ocurring breakdown would mark the emergence of an recordable experimental fact. In our case this would be a polaron (i.e. a localized electron surrounded by a distorted lattice) with a definite position. The reset would consist in extracting from the last valid multi-particle wave function the 'most plausible few-particle content' and give all other particles the (non-entangled) wavefunctions which they would have without the visit of the electron. Replacing the pre-breakdown wave function by this extremely simplified wave function would free a huge amount of storage and would allows to execute strict quantum mechanical time-evolution until a potential breakdown asks again for a reset.
I hope to learn from the RG-community
1. whether this or similar concepts were discussed elsewhere
2. how this obviously incomplete picture can be brought closer to completion.