When an electron is observed it acts like a particle and its wave function collapse. This statement is very famous in quantum mechanics, but what is meant by observing an electron? Which devices are used to do so, and by what technics?
If you mean observing like actually "seeing" an electron in a concrete way, that is not possible. Remember that when you "observe" in quantum mechanics, you produce a perturbation on the object; but you can see in spectroscopy the orbitals of atoms (that are stable wave functions of electrons), like orbital s or p, but using condensed matter instrumentation.