I looked into alpha decay where they set the decay constant equal to $vT/R$ with velocity $v$ and nuclear radius $R$. This seems to be very heuristically motivated with the image of having the alpha moving through the well and bouncing off the the barrier with prob. 1-T and tunneling through with prob. T. I wonder if that's the sort of semi-classicality that comes with WKB or whether there exists some rigorous quantum derivation. –  Jonas Jul 10 '13 at 9:13