Are Eigenfunctions and Eigenstates Just Eigenvectors?

[quasar_4]

So, I'm pretty sure this is trivial, but I just want to be sure:

My QM book frequently uses both the terms "eigenfunction" and "eigenstate". While they could connote slightly different physical references, they ARE both just eigenvectors, right?

I'm mostly a mathematician by training and am more familiar simply with "eigenvector". It's been bothering me that the two are the same mathematically, but I can't tell in which context they are using each name (they seem to be interchanged quite a bit, one problem refers to eigenstates, the next to eigenfunctions, but they're all just eigenvectors!).

Thanks.

quasar

 

[Avodyne]

Yes, these terms are pretty much used interchangably. To the extent that there is any distinction at all, "eigenstate" emphasizes that the object is the "quantum state" of the system, and so has physical significance; "eigenvector" emphasizes math over physics. And "eigenfunction" is used for the subclass of problems where the operator is a differential operator on functions on R^d (or something like that, I'm really bad at math terminology).

 

[newbee]

My QM book frequently uses both the terms "eigenfunction" and eigenstate". While they could connote slightly different physical references, they ARE both just eigenvectors, right?

Both are eigenvectors. In my experience the term "eigenfunction" is usually reserved for the configuration space representation of an eigenstate.