It is difficult to see something with dimensions 2.82×10-15 m or less*. But sometimes one can succeed – observing not exactly an electron but its path – an orbital. What was untill recently only a mathematic formula, a probability plot or just an artistic “shadowing”.
Now with the help of precisely planned experiments on X-ray scattering takes a shape of the real d-orbital - a coloured bagel with "ears".
Moreover, ultrafast lasers
(there are several in Milano) allow to trace the electron motion after being
ejected from an atom in an ultra short time (10-18 s).
The theory shows, that such electrons, for example coming from ionization process -
ejected from a hydrogen atom during collisions or detached from HCl-
anion 
behave similar to waves on the water surface, when a drop falls on
it 
*the so-called classical electron radius, determined with assumption that all the mass of electron comes from its electrostatic energy (and with using Einstein’s formula E=mc2)