What can this observable represent?

[OhNoYaDidn't]

## \hat{A}=
\begin{pmatrix}
1 &- 1 \\
-1&1
\end{pmatrix}
##
this is written in a basis ##\left ( |1>,|2> \right )##
So, i know this is an Hermitian operator, so it can represent an observable.
Can this operator represent an electric dipole moment? A momentum? A component of the orbital angular momentum?

1- for the momentum, i assume, since we can write ##\hat{p} ## as creation and annihilation operators, this would have no diagonal terms in this basis. What about the others, any suggestions?

Thank you!

 

[Mentz114]

## \hat{A}=
\begin{pmatrix}
1 &- 1 \\
-1&1
\end{pmatrix}
##
this is written in a basis ##\left ( |1>,|2> \right )##
So, i know this is an Hermitian operator, so it can represent an observable.
Can this operator represent an electric dipole moment? A momentum? A component of the orbital angular momentum?

1- for the momentum, i assume, since we can write ##\hat{p} ## as creation and annihilation operators, this would have no diagonal terms in this basis. What about the others, any suggestions?

Thank you!

It is ##\mathbf{1} - \sigma_x## where ##\sigma_x## is a Pauli spin matrix but I can't think what observable it could be.

 

[Zafa Pi]

## \hat{A}=
\begin{pmatrix}
1 &- 1 \\
-1&1
\end{pmatrix}
##
this is written in a basis ##\left ( |1>,|2> \right )##
So, i know this is an Hermitian operator, so it can represent an observable.
Can this operator represent an electric dipole moment? A momentum? A component of the orbital angular momentum?

1- for the momentum, i assume, since we can write ##\hat{p} ## as creation and annihilation operators, this would have no diagonal terms in this basis. What about the others, any suggestions?

Thank you!

It is singular and has one eigenvector [1,-1]. So it yields the probability a planer polarized photon will emerge from a polarized lens whose axis is at -45 degrees from the horizontal.
Here is a ? just in case I'm wrong.