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H

Comment: The classic example of half-life is radioactivity. In any sample of matter, some of the nuclei will be radioactive isotopes and the remainder not. The decline in the radioactivity of the sample is governed by a first-order Poisson process

N = N0e−λt where1 N and N0 are the current and original number of radioactive atoms in the sample and λ the characteristic decay constant for an isotope. Thus t1/2 = ln 2/λ. Judged by the metric of radioactivity, nonradioactivity is a nonobservable state (though it can of course be observed by other assays). Hamilton equations Let (q1, . . . , qn, p1, . . . , pn) be canonical coordinates and H a smooth function. Hamilton’s equations for H are

q˙ i = ∂H ∂p˙i

, p˙i = − ∂H

∂q˙i , i = 1, . . . , n.