Abstract
If the lifetime of a collision is defined as the difference between the times in which a particle moves in free space and under an interaction from a scattering center to the outside (or in the reverse direction), this paper shows that exactly the same relation between the lifetime operator Q and the scattering matrix S as was found by Smith (1960) can be derived. This can be done in a natural way provided that the time operator is defined as [Formula: see text] and the manifold of the asymptotic outgoing (or incoming) states is chosen to be the set of corresponding eigenstates. The part of the time needed for the particle moving freely from the scattering center to R is equal to R/v.
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