Editing Pauli exclusion principle (section)

{{Short description|Quantum mechanics rule: identical fermions cannot occupy the same quantum state simultaneously}}
[[File: Wolfgang Pauli young.jpg|right|200px|thumb|[[Wolfgang Pauli]] during a lecture in Copenhagen (1929).<ref>{{Cite web|url=http://cds.cern.ch/record/42709|title=Wolfgang Pauli during a lecture in Copenhagen|access-date=2023-09-11}}</ref> Wolfgang Pauli formulated the Pauli exclusion principle.]]
{{Quantum mechanics|cTopic=Fundamental concepts}}

In [[quantum mechanics]], the '''Pauli exclusion principle''' (German: '''Pauli-Ausschlussprinzip''') states that two or more [[identical particles]] with [[Fermion|half-integer spins]] (i.e. [[fermion]]s) cannot simultaneously occupy the same [[quantum state]] within a system that obeys the laws of [[quantum mechanics]]. This principle was formulated by Austrian physicist [[Wolfgang Pauli]] in 1925 for [[electron]]s, and later extended to all fermions with his [[spin–statistics theorem]] of 1940.

In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons  to have the same two values of ''all'' four of their [[quantum number]]s, which are: ''n'', the [[principal quantum number]]; ''{{ell}}'', the [[azimuthal quantum number]]; ''m<sub>{{ell}}</sub>'', the [[magnetic quantum number]]; and ''m<sub>s</sub>'', the [[spin quantum number]]. For example, if two electrons reside in the same [[atomic orbital|orbital]], then their values of ''n'', ''{{ell}}'', and ''m<sub>{{ell}}</sub>'' are equal. In that case, the two values of ''m''<sub>s</sub> (spin) pair must be different. Since the only two possible values for the spin projection ''m''<sub>s</sub> are +1/2 and −1/2, it follows that one electron must have ''m''<sub>s</sub> = +1/2 and one ''m''<sub>s</sub> = −1/2.

Particles with an integer spin ([[boson]]s) are not subject to the Pauli exclusion principle. Any number of identical bosons can occupy the same quantum state, such as photons produced by a [[laser]], or atoms found in a [[Bose–Einstein condensate]].

A more rigorous statement is: under the exchange of two identical particles, the total (many-particle) [[wave function]] is [[Identical particles#Quantum mechanical description of identical particles|antisymmetric]] for fermions and symmetric for bosons. This means that if the space ''and'' spin coordinates of two identical particles are interchanged, then the total wave function changes sign for fermions, but does not change sign for bosons.

So, if hypothetically two fermions were in the same state{{mdash}}for example, in the same atom in the same orbital with the same spin{{mdash}}then interchanging them would change nothing and the total wave function would be unchanged. However, the only way a total wave function can both change sign (required for fermions), and also remain unchanged is that such a function must be zero everywhere, which means such a state cannot exist. This reasoning does not apply to bosons because the sign does not change.