The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles. The principle was formulated by Austrian physicist Wolfgang Pauli in 1925.
For example, no two electrons in a single atom can have the same four quantum numbers; if n, l, and ml are the same, ms must be different such that the electrons have opposite spins, and so on.
Integer spin particles, bosons, are not subject to the Pauli exclusion principle: any number of identical bosons can occupy the same quantum state, as with, for instance, photons produced by a laser and Bose–Einstein condensate.
Read more about Pauli Exclusion Principle: Overview, History, Connection To Quantum State Symmetry
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