antisymmetric wave function

In quantum mechanics, a wave function describes the wave-like behavior of a particle. The square of the wave function indicates the probability of finding the particle in a specific location. For systems with identical particles, like electrons, the wave function must adhere to specific symmetry rules. If the coordinates of two identical particles are swapped, the wave function either remains unchanged (symmetric) or changes sign (antisymmetric).12

Particles with half-integral spin, such as electrons, protons, and neutrons, are called fermions and are characterized by antisymmetric wave functions. This property leads to the exclusion principle, which states that no two identical fermions can occupy the same quantum state.2