The Pauli exclusion principle is a quantum mechanical principle formulated by the Austrian physicist Wolfgang Pauli in 1925. In its simplest form for electrons in a single atom, it states that no two electrons can have the same four quantum numbers; that is, if n, l, and ml are the same, ms must be different such that the electrons have opposite spins. More generally, no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously. A more rigorous statement of this principle is that for two identical fermions, the total wave function is anti-symmetric.
In contrast, integer spin particles, bosons, are not subject to the Pauli exclusion principle. For bosons, any number of identical particles can occupy the same quantum state, as with, for instance, lasers and Bose-Einstein condensation.
The Pauli exclusion principle is one of the most important principles in physics, mainly because the three types of particles from which the ordinary atom is made—electrons, protons, and neutrons—are all subject to it; consequently, all material particles exhibit space-occupying behavior. The Pauli exclusion principle underpins many of the characteristic properties of matter, from the large-scale stability of matter to the existence of the periodic table of the elements.
Fermions, particles with antisymmetric wave functions, obey the Pauli exclusion principle. Apart from the familiar electron, proton and neutron, these include neutrinos and quarks (from which protons and neutrons are made), as well as some atoms like helium-3. All fermions possess "half-integer spin", meaning that they possess an intrinsic angular momentum whose value is (reduced Planck's constant) times a half-integer (1/2, 3/2, 5/2, etc.). In the theory of quantum mechanics, fermions are described by antisymmetric states. Particles with integer spin have a symmetric wave function and are called bosons; in contrast to fermions, they may share the same quantum states. Examples of bosons include the photon, the Cooper pairs (which are responsible for superconductivity), and the W and Z bosons.
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