Question

Think a slit experiment ala the double slit experiment. And then you make the hole theoretically small. Will the particle come through?

Answer 1

Well there is a limit to how small the hole can be. If the barrier is a solid it is made of atoms which remain fixed in position relative to one another. Taking only one of these atoms out would make the smallest possible hole. I'd say the electron could still go through. But also recall that if the barrier is thin enough, even if the electron does not have enough energy (classically) to do so, it can quantum tunnel to the other side, even if there is no hole at all.