  Long ago appeared a discussion in quantum mechanics of the problem of opening
a completely absorbing shutter on which were impinging a stream of particles of
definite velocity. The solution of the problem was obtained in a form entirely
analogous to the optical one of diffraction by a straight edge. The argument of
the Fresnel integrals was though time dependent and thus the first part in the
title of this article. In section 1 we briefly review the original formulation
of the problem of diffraction in time. In section 2 and 3 we reformulate
respectively this problem in Wigner distributions and tomographical
probabilities. In the former case the probability in phase space is very simple
but, as it takes positive and negative values, the interpretation is ambiguous,
but it gives a classical limit that agrees entirely with our intuition. In the
latter case we can start with our initial conditions in a given reference frame
but obtain our final solution in an arbitrary frame of reference.
