  We address the phenomenon of diffraction of non-relativistic matter waves on
openings in absorbing screens. To this end, we expand the full quantum
propagator, connecting two points on the opposite sides of the screen, in terms
of the free particle propagator and spatio-temporal properties of the opening.
Our construction, based on the Huygens-Fresnel principle, describes the quantum
phenomena of diffraction in space and diffraction in time, as well as the
interplay between the two. We illustrate the method by calculating diffraction
patterns for localized wave packets passing through various time-dependent
openings in one and two spatial dimensions.
