Why Fermions Have Antisymmetric Wave Function?

Particles which exhibit antisymmetric states are called fermions. Antisymmetry gives rise to the Pauli exclusion principle, which forbids identical fermions from sharing the same quantum state. ... It states that bosons have integer spin, and fermions have half-integer spin.

What does it mean for a wave function to be antisymmetric?

A wavefunction that is antisymmetric with respect to electron interchange is one whose output changes sign when the electron coordinates are interchanged, as shown below. ˆP12|ψ(r1,r2)⟩=−|ψ(r2,r1)⟩ These particles are called fermions and have half-integer spin and include electrons, protons, and neutrinos.

Why do electrons have antisymmetric function?

This arises from the electrostatic repulsion energy between the electrons. In the spatially antisymmetric state, the two electrons have zero probability of being at the same place, and are on average further apart than in the spatially symmetric state.