Editing Spin quantum number (section)

== Total spin of an atom or molecule ==
For some [[Atom|atoms]] the [[Electron magnetic moment|spins]] of several [[Unpaired electron|unpaired electrons]] ({{mvar|s}}{{sub|1}}, {{mvar|s}}{{sub|2}}, ...) are coupled to form a ''total spin'' [[quantum number]] {{mvar|S}}.<ref name=Merzbacher>{{cite book |author-link=Eugen Merzbacher |author=Merzbacher, E. |year=1998 |title=Quantum Mechanics |edition=3rd |publisher=John Wiley |pages=430–431 |isbn=0-471-88702-1}}</ref><ref name=Atkins>{{cite book |author1-link=Peter Atkins |author1=Atkins, P. |author2=de&nbsp;Paula, J. |year=2006 |title=Physical Chemistry |edition=8th |publisher=W.H. Freeman |page=352 |isbn=0-7167-8759-8}}</ref> This occurs especially in light atoms (or in [[Molecule|molecules]] formed only of light atoms) when [[spin–orbit coupling]] is weak compared to the coupling between spins or the coupling between orbital [[Angular momentum|angular momenta]], a situation known as [[Angular momentum coupling#LS coupling|{{math|L S}} coupling]] because {{mvar|L}} and {{mvar|S}} are [[Constant of motion|constants of motion]]. Here {{mvar|L}} is the total ''orbital'' angular momentum quantum number.<ref name=Atkins/>

For atoms with a well-defined {{mvar|S}}, the [[Multiplicity (chemistry)|multiplicity]] of a state is defined as {{nobr| 2{{mvar|S}} + 1}}. This is equal to the number of different possible values of the total (orbital plus spin) angular momentum {{mvar|J}} for a given ({{mvar|L}}, {{mvar|S}}) combination, provided that {{mvar|S}} ≤ {{mvar|L}} (the typical case). For example, if {{mvar|S}} = 1, there are three states which form a [[triplet state|triplet]]. The [[Eigenvalues and eigenvectors|eigenvalues]] of {{mvar|S{{sub|z}}}} for these three states are {{math|+1ħ, 0,}} and {{math|−1ħ}}.<ref name=Merzbacher/> The [[term symbol]] of an atomic state indicates its values of {{mvar|L}}, {{mvar|S}}, and {{mvar|J}}.

As examples, the ground states of both the [[Oxygen|oxygen atom]] and the [[Triplet oxygen|dioxygen molecule]] have two unpaired electrons and are therefore triplet states. The atomic state is described by the term symbol {{sup|3}}P, and the molecular state by the term symbol {{sup|3}}Σ{{su|b=g|p=−}} where the superscript "3" indicates the multiplicity.