Editing Fock state (section)

==Example using two particles==
For any final state <math>|f\rangle</math>, any Fock state of two identical particles given by <math>|1_{{\mathbf{{k}}_1}}, 1_{{\mathbf{{k}}_2}}\rangle</math>, and any [[Operator (physics)|operator]] <math> \widehat{\mathbb{O}} </math>, we have the following condition for [[Identical particles|indistinguishability]]:<ref name=FGross>{{Cite book
|last= Gross
|first= Franz
|title= Relativistic Quantum Mechanics and Field Theory
|publisher= Wiley-VCH
|date= 1999
|isbn= 0471353868
}}</ref>{{rp|191}}
: <math>
  \left|\left\langle f\left|\widehat{\mathbb{O}}\right|1_{\mathbf{k}_1}, 1_{\mathbf{k}_2}\right\rangle\right|^2 =
  \left|\left\langle f\left|\widehat{\mathbb{O}}\right|1_{\mathbf{k}_2}, 1_{\mathbf{k}_1}\right\rangle\right|^2
</math>.

So, we must have <math>\left\langle f\left|\widehat{\mathbb{O}}\right|1_{{\mathbf{{k}}_1}}, 1_{{\mathbf{{k}}_2}}\right\rangle = e^{i\delta}\left\langle f\left|\widehat{\mathbb{O}}\right|1_{{\mathbf{{k}}_2}}, 1_{{\mathbf{{k}}_1}}\right\rangle</math>

where <math>e^{i\delta} = +1</math> for [[bosons]] and <math>-1</math> for [[fermions]]. Since <math>\langle f| </math> and <math>\widehat{\mathbb{O}}</math> are arbitrary, we can say, 
: <math>\left|1_{\mathbf{k}_1}, 1_{\mathbf{k}_2}\right\rangle = +\left|1_{\mathbf{k}_2}, 1_{\mathbf{k}_1}\right\rangle</math> for bosons and 
: <math>\left|1_{\mathbf{k}_1}, 1_{\mathbf{k}_2}\right\rangle = -\left|1_{\mathbf{k}_2}, 1_{\mathbf{k}_1}\right\rangle</math> for fermions.<ref name=FGross/>{{rp|191}}

Note that the number operator does not distinguish bosons from fermions; indeed, it just counts particles without regard to their symmetry type. To perceive any difference between them, we need other operators, namely the [[creation and annihilation operators]].