RE: Matter waves - a central concept in quantum mechanics
Particle wave duality is one of those concepts in which the effective transition limit between both representations is really not that well understood I think.
It is similar to the transition between deterministic and statistical (quantum) many particle mechanics. I.e. when do entropy and thermodynamics really enter the picture, where is the effective limit and so on...
I mean some knowledge exists but it is sadly not very common in the literature :D