  We reanalyse the time evolution of the $K^0-\bar{K^0}$ system in the language
of certain spectral function whose Fourier transforms give the time dependent
survival and transition amplitudes. The reanalysis turned out to be necessary
in view of the astonishing theorem by Khalfin on the possibility of vacuum
regeneration of $K_S$ and $K_L$. The main reason for this unexpected behaviour
is the non-orthogonality of $\ks$ and $\kl$. As a result of this theorem new
contributions to the well known oscillatory terms will enter the time dependent
transition probabilities. These new terms are not associated with small/large
time behaviour of the amplitudes and therefore their magnitude is apriori
unknown. Approximating the spectral functions by an one-pole ansatz Khalfin
estimated the new effect in transition probabilities to be $4 \times 10^{-4}$.
Whereas we agree with Khalfin on the general existence of vacuum regeneration
of $K_S$ and $K_L$ we disagree on the size of the effect. A careful analysis of
the one-pole approximation reveals that the effect is eleven orders of
magnitude smaller than Khalfin's estimate and, in principle, its exact
determination lies outside the scope of the one-pole ansatz. The present paper
gives also insight into the limitation of the validity of one-pole
approximation, not only for small/large time scales, but also for intermediate
times where new effects, albeit small, are possible. It will be shown that the
same validity restrictions apply to the known formulae of Weisskopf-Wigner
approximation as well.
