Editing Spin quantum number (section)

== Nomenclature ==
[[File:Quantum projection of S onto z for spin half particles.svg|thumb|Quantum projection of S onto z for spin half particles]]
The phrase ''spin quantum number'' refers to quantized [[spin (physics)|spin angular momentum]]. 
The symbol {{mvar|s}} is used for the spin quantum number, and {{mvar|m{{sub|s}}}} is described as the spin magnetic quantum number<ref>{{cite book | last1=Atkins | first1=Peter |last2=de&nbsp;Paula | first2=Julio | year=2006 | title=Atkins' Physical Chemistry |edition=8th | publisher=W.H. Freeman | isbn=0-7167-8759-8 |page=308}}</ref> or as the {{mvar|z}}-component of spin {{mvar|s{{sub|z}}}}.<ref>{{cite book | last1=Banwell | first1=Colin N. | last2=McCash | first2=Elaine M. | year=1994 | title=Fundamentals of Molecular Spectroscopy | publisher=McGraw-Hill | isbn=0-07-707976-0 | page=135}}</ref>

Both the total spin and the z-component of spin are quantized, leading to two quantum numbers spin and spin magnet quantum numbers.<ref name="Peterson 1989">{{cite journal | last1=Perrino | first1=Charles T. | last2=Peterson | first2=Donald L. | title=Another quantum number? | journal=J. Chem. Educ. | volume=66 | issue=8 | year=1989 | issn=0021-9584 | doi=10.1021/ed066p623 | page=623| bibcode=1989JChEd..66..623P }}</ref> The (total) spin quantum number has only one value for every elementary particle. Some introductory chemistry textbooks describe {{mvar|m{{sub|s}}}} as the ''spin quantum number'',<ref>{{cite book |last1=Petrucci |first1=Ralph H. |last2=Harwood |first2=William S. |last3=Herring |first3=F. Geoffrey |year=2002 |title=General Chemistry |edition=8th |publisher=Prentice Hall |isbn=0-13-014329-4 |page=333}}</ref><ref>{{cite book |last1=Whitten |first1=Kenneth W. |last2=Galley |first2=Kenneth D. |last3=Davis |first3=Raymond E. |year=1992 |title=General Chemistry |edition=4th |publisher=Saunders College Publishing |isbn=0-03-072373-6 |page=196}}</ref> and {{mvar|s}} is not mentioned since its value {{sfrac|1|2}} is a fixed property of the electron; some even use the variable {{mvar|s}} in place of {{mvar|m{{sub|s}}}}.<ref name="Peterson 1989" /> 

The two spin quantum numbers <math>s</math> and <math>m_s</math> are the spin angular momentum analogs of the two [[azimuthal quantum number |orbital angular momentum quantum number]]s <math>l</math> and <math>m_l</math>.<ref>Karplus, Martin, and Porter, Richard Needham. Atoms and Molecules. United States, W.A. Benjamin, 1970.</ref>{{rp|152}}

Spin quantum numbers apply also to systems of coupled spins, such as atoms that may contain more than one electron. Capitalized symbols are used: {{mvar|S}} for the total electronic spin, and {{mvar|m}}<sub>{{mvar|S}}</sub> or {{mvar|M}}<sub>{{mvar|S}}</sub> for the {{mvar|z}}-axis component. A pair of electrons in a spin [[singlet state]] has {{mvar|S}} = 0, and a pair in the [[triplet state]] has {{mvar|S}} = 1, with {{mvar|m}}<sub>{{mvar|S}}</sub> = −1, 0, or +1. Nuclear-spin quantum numbers are conventionally written {{mvar|I}} for spin, and {{mvar|m}}<sub>{{mvar|I}}</sub> or {{mvar|M}}<sub>{{mvar|I}}</sub> for the {{mvar|z}}-axis component.

The name "spin" comes from a geometrical [[Spin (geometry)|spinning]] of the electron about an axis, as proposed by [[George Uhlenbeck|Uhlenbeck]] and [[Samuel Goudsmit|Goudsmit]]. However, this simplistic picture was quickly realized to be physically unrealistic, because it would require the electrons to rotate faster than the speed of light.<ref>{{cite news |last=Halpern |first=Paul |date=2017-11-21 |title=Spin: The quantum property that should have been impossible |series=Starts with a bang |magazine=[[Forbes]] |url=https://www.forbes.com/sites/startswithabang/2017/11/21/spin-the-quantum-property-that-nature-shouldnt-possess/ |access-date=2018-03-10|archive-url=https://web.archive.org/web/20180310202714/https://www.forbes.com/sites/startswithabang/2017/11/21/spin-the-quantum-property-that-nature-shouldnt-possess/ |archive-date=2018-03-10}}</ref> It was therefore replaced by a more abstract quantum-mechanical description.