Does quantum mechanics predict that there is any probability of finding excess charge inside a conductor?
I've read an explanation about the distribution of excess charge placed on conductors. The explanation says that at electrostatic equilibrium, all of the excess charge migrates to the surface of the conductor. The justification for this is that if any excess charged was found locally inside the conductor, then a Gaussian surface around the charge would imply an electric field flux and perpetual movement of charge.
However, I also know that quantum mechanics predicts that electrons are delocalized around a nucleus with a probability function for being at any arbitrary distance away from the nucleus, even for the lowest energy level. I've also read that electrons can tunnel through energy barriers.