- #1

jostpuur

- 2,116

- 19

Can somebody give an example of two matrices [itex]a_1[/itex] and [itex]a_2[/itex] which would satisfy the relation

[tex]

a_i a_j^{\dagger} + a_j^{\dagger} a_i = \delta_{ij}

[/tex]

I know that

[tex]

\left(\begin{array}{cc}

0 & 1 \\ 0 & 0 \\

\end{array}\right)

\left(\begin{array}{cc}

0 & 0 \\ 1 & 0 \\

\end{array}\right)

+ \left(\begin{array}{cc}

0 & 0 \\ 1 & 0 \\

\end{array}\right)

\left(\begin{array}{cc}

0 & 1 \\ 0 & 0 \\

\end{array}\right)

= 1

[/tex]

but I found myself unable to modify this for the index [itex]i\in\{1,2\}[/itex].

[tex]

a_i a_j^{\dagger} + a_j^{\dagger} a_i = \delta_{ij}

[/tex]

I know that

[tex]

\left(\begin{array}{cc}

0 & 1 \\ 0 & 0 \\

\end{array}\right)

\left(\begin{array}{cc}

0 & 0 \\ 1 & 0 \\

\end{array}\right)

+ \left(\begin{array}{cc}

0 & 0 \\ 1 & 0 \\

\end{array}\right)

\left(\begin{array}{cc}

0 & 1 \\ 0 & 0 \\

\end{array}\right)

= 1

[/tex]

but I found myself unable to modify this for the index [itex]i\in\{1,2\}[/itex].

Last edited: