Editing Spin–statistics theorem (section)

{{short description|Theorem in quantum mechanics}}
{{Statistical mechanics|cTopic=[[Particle statistics|Particle Statistics]]}}The '''spin–statistics theorem''' proves that the observed relationship between the [[Spin (physics)|intrinsic spin]] of a particle ([[angular momentum]] not due to the orbital motion) and the quantum [[particle statistics]] of collections of such particles is a consequence of the mathematics of [[quantum mechanics]].

According to the theorem, the many-body [[wave function]] for [[elementary particle]]s with integer spin ([[bosons]]) is symmetric under the exchange of any two particles, whereas for particles with half-integer spin ([[fermions]]), the wave function is antisymmetric under such an exchange. A consequence of the theorem is that non-interacting particles with integer spin obey [[Bose–Einstein statistics]], while those with half-integer spin obey [[Fermi–Dirac statistics]].<ref>{{Cite book |last=Leggett |first=Anthony J. |title=Quantum liquids: Bose condensation and Cooper pairing in condensed-matter systems |date=2006 |publisher=Oxford University Press |isbn=978-0-19-171195-4 |series=Oxford graduate texts|pages=5,8-10}}</ref><ref>{{Cite book |title = The Principles of Quantum Mechanics |url = https://books.google.com/books?id=XehUpGiM6FIC |publisher = Clarendon Press |date = 1981-01-01 |isbn = 9780198520115 |language = en |first = Paul Adrien Maurice |last = Dirac |page = 149}}</ref><ref>{{Cite book |title = General principles of quantum mechanics |url = https://books.google.com/books?id=A84NAQAAIAAJ |publisher = Springer-Verlag |date = 1980-01-01 |isbn = 9783540098423 |language = en |first = Wolfgang |last = Pauli}}</ref>