Creation and annihilation operators
= Creation and annihilation operators
{wiki}
The bosonic ladder operators satisfy
$$
[A,A^\dagger]=1,
\qquad
A|n\rangle=\sqrt n\,|n-1\rangle,
\qquad
A^\dagger|n\rangle=\sqrt{n+1}\,|n+1\rangle.
$$
= Creation and annihilation operators
{wiki}
The bosonic ladder operators satisfy
$$
[A,A^\dagger]=1,
\qquad
A|n\rangle=\sqrt n\,|n-1\rangle,
\qquad
A^\dagger|n\rangle=\sqrt{n+1}\,|n+1\rangle.
$$