A simple model for radioactive decay of an unstable nuclear isotope is as follows.3 Consider the potential illustrated in Fig. 7.9, in which there is a hard, infinite barrier at the spatial origin, a finite barrier of width Δx starting at x = a with height V0, and the potential everywhere else 0. We can model this nucleus as a particle initially located in the “bound” region with energy E, where 0 a+Δx. Once a large fraction of the wavefunction has exited the bound region, say 1/2 of the probability of the particle’s position, then we can say that the nucleus decayed. In this example, we would like to determine, or at least estimate, the time it takes for the nucleus to decay.

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