Is it meaningful in quantum mechanics to speak of charge distribution? Some people say if you sovle the Schroedinger Equation for the hydrogen atom, the eigenfunctions represent a type of charge density...that is, the square of the amplitude is a charge density. Yes, I know some people say it's not charge density, it's just the probability of finding an electron, but let's just call it charge density. That's not the point.
The point is: in more complex systems, does quantum mechanics recognize the existence of a similar quantity to the square of the amplitude in the hydrogen atom...a generalized charge density? or at least, a probability of finding charge. If I look at a glass of water, can I say that according to quantum mechanics, for any given point (x,y,z) there is a certain expectation dQ within any given volume element dV that there is a unit charge within that volume?
Or, as certain correspondents have claimed in a related question which was shut down by the moderators, is it meaningless in quantum mechanics to talk about such a quantity dQ/dV?