The Tunnel Effect
The wave associated with an alpha particle trapped inside a nucleus has been superimposed to the previous figure. We see that the wave extends slightly outside the nucleus, where the oscillation amplitude has been amplified to make them visible. The square of the amplitude of the oscillations is, in quantum mechanics, the probability of observing the particle at a given position. So there is a probability of observing the alpha particle outside the nucleus, that is to say a decay.
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