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We study the quantum slit diffraction problem in three dimensions. In thetreatment of diffraction of particles by a slit, it is usually assumed that themotion perpendicular to the slit is classical. Here we take into account theeffect of the quantum nature of the motion perpendicular to the slit using theGreen function approach [18]. We treat the diffraction of a Gaussian wavepacket for general boundary conditions on the shutter. The difference betweenthe standard and our three-dimensional slit diffraction models is analogous tothe diffraction in time phenomenon introduced in [16]. We derive corrections tothe standard formula for the diffraction pattern, and we point out situationsin which this might be observable. In particular, we discuss the diffraction inspace and time in the presence of gravity.

Three-dimensional Quantum Slit Diffraction and Diffraction in Time