Abstract
The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the resulting patterns depend on a quasi-time τ given by a function of the coordinate along the propagation axis in a classical combination z₀-t² F/m, while the diffraction effects along transverse axes are due solely to m/ℏ. The consequences on the precision at which the equivalence principle can be tested are discussed. Realizations with ultra cold neutrons, Bose-Einstein condensates and molecular beams are proposed.