Would there be an upper limit to density in QM?

[benorin]

Admitted I know very little about QM, but I've been thinking about black holes and I wondered if there would be an upper limit to density of an object of the smallest size allowable if the particles are not being observed by anyone (since black holes are black)? I ignorantly wondered that classically perhaps even though an atom is 99.99% empty space or so there seemly would be a logical upper limit to the density of an object because 0.01% of that atom is not empty but in QM all is waves and probability so this might not be the case here. Please make your answers understandable (I've taken a standard 3 semester sequence course of physics and math through analysis). Thanks for your time physicists, hope you don't mind a noob question.

 

[Nugatory]

As far as quantum mechanics (and also classical mechanics with its point particles) is concerned, there is no upper limit to the density of an object.
However, nether of these theories have been tested at arbitrarily high densities and it's quite likely that some as-yet-unknown physics will come into play at some point.

So the answer to your question is basically "as far as we know QM doesn't enforce a limit, but that doesn't mean there isn't one".

 

[benorin]

It's been 10+ years since I took physics in college and clearly I've forgotten some things (thanks for being kind) but I remember the particle in a box lecture quite well (barrier tunneling). Could this approach be applied to particle in a black hole? Because when I think what in nature might qualify as an infinite potential wall I think the event horizon of a black hole might just be it.

 

[Nugatory]

Could this approach be applied to particle in a black hole? Because when I think what in nature might qualify as an infinite potential wall I think the event horizon of a black hole might just be it.

No. The event horizon of a black hole is nothing like a wall or barrier.