How does the wave-particle duality of electrons explain the phenomenon of electron interference observed in double-slit experiments, and how is this related to the wavefunction?

Electrons act both as particles and as waves; when a single electron is fired at a double‑slit screen, its associated wavefunction splits and travels through both slits simultaneously, forming a superposition. The two parts of the wavefunction overlap and interfere, creating regions where the waves add (constructive interference) and cancel (destructive interference). When the electron finally lands on the detector screen, the probability of finding it is given by the squared magnitude of the combined wavefunction, so over many electrons a bright‑dark interference pattern appears. Thus the interference pattern is a direct manifestation of the electron’s wave nature encoded in its wavefunction. In practice, one electron at a time still builds the pattern, showing that the wavefunction governs the statistical distribution of particle impacts.