- #1

- 488

- 4

Suppose a proudct is form by a Fock state [tex]|n\rangle[/tex] and any other state [tex]|x\rangle[/tex], i.e.

[tex]|\phi\rangle = |n\rangle|x\rangle[/tex]

If an operator defined as

[tex]

A = \left(

\begin{matrix}

\alpha\hat{a}\hat{a}^\dagger & \beta\hat{a}^\dagger\hat{a} \\

\gamma\hat{a}^\dagger\hat{a} & \kappa\hat{a}\hat{a}^\dagger

\end{matrix}

\right)

[/tex]

where [tex]\hat{a}[/tex] and [tex]\hat{a}^\dagger[/tex] is creation and annilation operator will only opeate on Fock state. So how A operate on [tex]|n\rangle|x\rangle[/tex]?

[tex]|\phi\rangle = |n\rangle|x\rangle[/tex]

If an operator defined as

[tex]

A = \left(

\begin{matrix}

\alpha\hat{a}\hat{a}^\dagger & \beta\hat{a}^\dagger\hat{a} \\

\gamma\hat{a}^\dagger\hat{a} & \kappa\hat{a}\hat{a}^\dagger

\end{matrix}

\right)

[/tex]

where [tex]\hat{a}[/tex] and [tex]\hat{a}^\dagger[/tex] is creation and annilation operator will only opeate on Fock state. So how A operate on [tex]|n\rangle|x\rangle[/tex]?

Last edited: