# When is a given state an eigenstate of a given operator?

## Main Question or Discussion Point

How do I know if some given state is and eigenstate of some given operator?

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HAYAO
Gold Member
This is an extremely broad question. Are you talking about experiments or theory?

I am referring to theory. I may have posted this in the wrong category as well, I'm not sure. But I'm trying to prove that some given state is not an eigenstate of some given operator. I'm doing this all in Dirac notation and matrix representation. So, should I start with the eigenvalue equation and show that the given state is not an eigenvector of the operator (Again, I know the operator and the state in matrix form)?

Nugatory
Mentor
So, should I start with the eigenvalue equation and show that the given state is not an eigenvector of the operator (Again, I know the operator and the state in matrix form)?
Yes, although it may be easier to assume that it is and then derive the result that the eigenvalue is zero.

Thank you for the help Nugatory, much appreciated.