What characterizes fermions when forming quantum states?

Fermions are characterized by obeying the Pauli Exclusion Principle, which states that no two identical fermions can occupy the same quantum state simultaneously. This principle leads to the requirement that the overall wave function for a system of identical fermions must be antisymmetric with respect to the exchange of any two particles.

When two fermions are exchanged, the wave function changes sign. This antisymmetry is crucial for the behavior of fermions, such as electrons in atoms, which fill up available quantum states and lead to the structure of the periodic table and the properties of matter. Therefore, when forming composite quantum states, fermions must exhibit these antisymmetrical properties.