I was wondering if I can say to a layman that "upon throwing the ball on a wall an enormously large number of times, there is a small probability that the ball will go through the wall", while explaining quantum tunneling (alpha decay example is abstract and artificial for a layman).
My doubt if whether the wall region can be modeled as a finite potential barrier (infinite potential barrier – which is not of Dirac delta form – will not allow tunneling).
Also, the wall seems to have all the other characteristics of the artificial barrier potential we set up in quantum mechanics, am I missing anything?
Best Answer
isn't quite right. A barrier where there's a finite region of infinite potential will not allow tunneling, nor will potentials with singularities going suffiently fast $\to \infty$. But it's easy to construct a non-dirac potential with singularity that still permits tunneling; in particular the one-dimensional singularities of the $\tfrac{1}{|r|}$ peaks as which you might model the nuclei's coulomb potential aren't much of a problem. You can basically model the ball's CM amplitude as a Bloch wave there.
So, yes, a macroscopic ball can in fact tunnel through a brick wall. Of course, the probability is exponentially small in the thickness, so indeed an enourmously large number of throws is required. More problematically, it is far more likely for the ball to, say, spontaneously disintegrate into two identically-shaped halfs, to develop a tight chemical connection to the wall, or perhaps catch fire.