# What can this observable represent?

• I
In summary, the given matrix represents an Hermitian operator in the basis of |1> and |2>, making it a possible observable. However, it is unclear if it can represent an electric dipole moment, a momentum, or a component of the orbital angular momentum. It is noted that for momentum, the lack of diagonal terms in this basis may be a factor. One suggestion is that it could represent the probability of a planer polarized photon emerging from a polarized lens at a specific angle.
## \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:
## \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.

## \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.

## 1. What can this observable represent?

This question is asking about the potential interpretations or meanings of a specific observable in an experiment or study. The observable could represent a physical property, a behavior, a phenomenon, or any other aspect that can be measured or observed.

## 2. How do you determine what an observable represents?

The determination of what an observable represents is typically based on a combination of scientific theories, prior research, and experimental evidence. Scientists use a variety of methods, such as statistical analysis and control groups, to make conclusions about the meaning of an observable.

## 3. Can an observable have multiple representations?

Yes, an observable can have multiple representations or meanings. This is because scientific theories and interpretations can change over time as new evidence is discovered. Additionally, different researchers or scientists may have different interpretations of the same observable based on their perspectives and biases.

## 4. How does the context of an experiment affect what an observable represents?

The context of an experiment can greatly influence the interpretation of an observable. For example, the same observable may have different meanings or implications in a laboratory setting versus a real-life setting. The conditions and variables of an experiment can also impact the interpretation of an observable.

## 5. Are there any limitations to what an observable can represent?

Yes, there are limitations to what an observable can represent. Observables are based on measurements and observations, which are subject to human error and limitations. Additionally, there may be factors that cannot be measured or observed, making it difficult to fully understand the true meaning of an observable.

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