I What can this observable represent?

1. Jan 7, 2017

$\hat{A}= \begin{pmatrix} 1 &- 1 \\ -1&1 \end{pmatrix}$
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!

Last edited: Jan 7, 2017
2. Jan 7, 2017

Mentz114

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

3. Jan 8, 2017

Zafa Pi

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.