Editing Fock state (section)

===Action on some specific Fock states===
{{unordered list
| For a vacuum state—no particle is in any state— expressed as <math> |0_{{\mathbf{k}}_{1}},  0_{{\mathbf{k}}_{2}}, 0_{{\mathbf{k}}_{3}}...0_{{\mathbf{k}}_{l}}, ...\rangle</math>, we have:
: <math>b^{\dagger}_{{\mathbf{k}}_l}|0_{{\mathbf{k}}_{1}}, 0_{{\mathbf{k}}_{2}}, 0_{{\mathbf{k}}_{3}}...0_{{\mathbf{k}}_{l}}, ...\rangle = |0_{{\mathbf{k}}_{1}}, 0_{{\mathbf{k}}_{2}}, 0_{{\mathbf{k}}_{3}}...1_{{\mathbf{k}}_{l}}, ...\rangle </math>

and, <math>b_{\mathbf{k}_l}|0_{\mathbf{k}_1}, 0_{\mathbf{k}_2}, 0_{\mathbf{k}_3}...0_{\mathbf{k}_l}, ...\rangle = 0</math>.<ref name="TIFR"/>  That is, the ''l''-th creation operator creates a particle in the ''l''-th state '''k'''<sub>l</sub>, and the vacuum state is a fixed point of annihilation operators as there are no particles to annihilate.
| We can generate any Fock state by operating on the vacuum state with an appropriate number of '''creation operators''':
: <math>|n_{\mathbf{k}_1}, n_{\mathbf{k}_2} ...\rangle =
  \frac{\left(b^\dagger_{\mathbf{k}_1}\right)^{n_{\mathbf{k}_1}}}{\sqrt{n_{\mathbf{k}_1}!}}
  \frac{\left(b^\dagger_{\mathbf{k}_2}\right)^{n_{\mathbf{k}_2}}}{\sqrt{n_{\mathbf{k}_2}!}}...|0_{\mathbf{k}_{1}}, 0_{\mathbf{k}_{2}}, ...\rangle
</math>
| For a single mode Fock state, expressed as, <math>|n_\mathbf{k}\rangle</math>,
: <math>b^\dagger_\mathbf{k}|n_\mathbf{k}\rangle = \sqrt{n_\mathbf{k} + 1} |n_\mathbf{k} + 1\rangle</math> and, 
: <math>b_\mathbf{k}|n_\mathbf{k}\rangle = \sqrt{n_\mathbf{k}} |n_\mathbf{k} - 1\rangle</math>
}}