Single-Slit Electron Diffraction
Electrons with well-defined momentum (px=0) are localized in the x-direction by a slit of width Dx.
Interaction with the slit inevitably scatters the electrons, creating a spread in px of width Dx/h.
The distribution in direction after passing through the slit is the same as single-slit diffraction of light.
Notes:
This is a thought experiment, but real experiments like it have been done.
On the left of the slit, the x-component of the position of any electron in the beam is completely uncertain, so the direction of motion of the electrons is completely certain.
In order to pass through the slit, the electron has to have a known position, with uncertainty equal to the width of the slit. However, to get through the slit, the electrons have to interact with the quantized atoms of the slit material, producing a scattering into a range of directions, thus destroying the certainty in x-component of momentum.
Detailed analysis of the distributions in where the electrons land shows that the electrons form a single slit diffraction pattern just like light with the wavelength p/h.