# Quantum tunneling and a football permeating a wall

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?

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infinite potential barrier – which is not of Dirac delta form – will not allow tunneling

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.

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Can you elaborate how you deduced that "it is far more likely for the ball to, say, spontaneously disintegrate into two identically-shaped halfs" –  Bogo May 27 '13 at 12:15
That's more of a rough estimate, the idea being that for the ball to split only $\mathcal{O}(n^{2/3})$ atoms are involved in a "tunneling" process for which there is easily enough energy available from thermal excitations, at only the length scale of molecular bounds. Through the wall, we have $\mathcal{O}(n)$ atoms tunneling a macroscopic distance. –  leftaroundabout May 27 '13 at 12:28