How does the wave-like behavior of electrons relate to their probability density in a double-slit experiment?

Electrons behave like waves, described mathematically by a wavefunction that spreads out in space. The probability density of finding an electron at a particular spot is the square of the wavefunction’s amplitude, so it tells us where the electron is most likely to appear. In a double‑slit experiment, the electron’s wavefunction passes through both slits, and the two emerging waves overlap and interfere, creating regions where the waves add (constructive interference) and where they cancel (destructive interference). These regions translate directly into a pattern of high and low probability densities, producing bright and dark fringes on a screen. When you fire many single electrons, each lands randomly, but over time the spots accumulate into the familiar interference pattern, confirming that the wave‑like behavior governs the probability distribution.