Is there such a thing as charge density in quantum mechanics?

Is there such a thing as a time-varying charge density in quantum mechanics? I am looking at the tungsten filament in a light bulb. Am I allowed to say that there is a wave function which describes that filament, and that in some sense there is a time-varying charge density (which some people call a probability) associated with the square of that wave function? There are electrons which have a probability distribution, and there are nuclei which are vibrating within the lattice, but all in all is there, or is there not, a time-varying charge distribution associated with that glowing filament? And if not, why not?

EDIT: There seems to be some question as to just what kind of charge-density fluctuations I am talking about. Let me clarify: in a hydrogen atom in the ground state, I would say there are NO charge density fluctuations. But if there is a superposition of the ground state and a 2p state, I would say the charge distribution fluctuates sinusoidally at the difference frequency of the two states. THAT is the kind of charge density fluctuation I am asking about for in the tungsten filament. Does it or doesnt' it?

I hope this clarifies the intent of my question.

RE-EDIT: In a separate (and rather hard-fought) discussion, it appears that people who know more than me agree that there is indeed an oscillating charge distribution in the hydrogen superposition as described above (see Is there oscillating charge in a hydrogen atom? ).

So if there is an oscillating charge in the hydrogen atom, why wouldn't there be oscillating charge in a heated tungsten filament?