Symmetric and Antisymmetric Wave Functions

In quantum mechanics, the symmetry of a wave function depends on

that type of particle (bosons vs fermions)

Bosons (interaction mediators)

have integer spin, if you swap two identical bosons, the wave function remains unchanged.

Bose-Einstein states that

multiple bosons can occupy the same quantum state

Fermions

half integer spin, if you swap two identical fermions, the wave function changes sign (-), If both fermions are in the same quantum state, the wave function vanishes, which is impossible in reality.Pau

Pauli-Exclusion Principle

no two identical fermions can occupy the same quantum state at the same time. this principle explains why electrons in atoms fill energy states one by one instead of piling into the same state.