Pauli exclusion principleprinciple

The Pauli exclusion principle is a rule of the quantum world that forbids two particles from being in the same state at the same time. Imagine a theater where each seat has a unique row and seat number. Fermion spectators (such as electrons) cannot sit in the same seat together: each needs its own. Thanks to this, atoms do not collapse, and chemical elements differ from each other.

In 1925, Wolfgang Pauli formulated the exclusion principle to explain the structure of atomic spectra. The essence is simple: in a quantum system, two particles with half-integer spin (fermions) cannot be in the same quantum state. Behind the ornate formulation lies a deep idea: quantum states can be imagined as "apartments" with different sets of "keys" (quantum numbers), and no more than one fermion can be placed in one apartment. This is radically different from the behavior of bosons, which can "crowd" into one state.

The Pauli exclusion principle (Pauli's exclusion principle) is a fundamental principle of quantum mechanics stating that two or more identical fermions (particles with half-integer spin) cannot simultaneously occupy the same quantum state within a single quantum system. Mathematically, this is expressed by the antisymmetry of the wave function: when two fermions are swapped, the wave function changes sign. For bosons, by contrast, the wave function is symmetric. The principle explains the structure of electron shells of atoms, the properties of metals and neutron stars, and also underlies Fermi–Dirac statistics.