Number state
= Number state
{title2=$|n\rangle$}
A number state is a normalized <eigenstate> of the <number operator>:
$$
N|n\rangle=n|n\rangle,
\qquad n\in\mathbb Z_{\geq0}.
$$
For a single <quantum harmonic oscillator>, it is also an <energy eigenstate> with energy $\hbar\omega(n+1/2)$.