What is the quantum mechanical difference between an eigenstate/function/vector?

[jeebs]

I see these terms used a lot and at times they seem to be used interchangeably. I am aware of the eigenvalue equation being applied to the normal expression of operators or their matrix versions, eg. Hu = \lambda \lambda u but I see this thing called u being referred to as eigenstate, eigenfunction or eigenvector (or sometimes even just vector) all the time.
What's the deal with this?
Thanks.

[phyzguy]

You're right, these terms are used interchangably.

[jeebs]

You're right, these terms are used interchangably.

but why, this surely causes needless confusion?

[phyzguy]

These things are not really under anyone's control - different terms just start up and get perpetuated. That's the way language is. There are many examples of things like this - physicists and mathematicians use different terms and different conventions for the same things in many cases. Look at all of the different conventions for Fourier transforms, for example - some people put the 2*pi in one place, some in another. Or why do some people use a (+---) metric signature and other people use a (-+++) signature? Or why do I call it a wrench, while the Brits call it a spanner? All you can do is live with it and become comfortable with the different terms.

[jeebs]

These things are not really under anyone's control - different terms just start up and get perpetuated. That's the way language is. There are many examples of things like this - physicists and mathematicians use different terms and different conventions for the same things in many cases. Look at all of the different conventions for Fourier transforms, for example - some people put the 2*pi in one place, some in another. Or why do some people use a (+---) metric signature and other people use a (-+++) signature? Or why do I call it a wrench, while the Brits call it a spanner? All you can do is live with it and become comfortable with the different terms.

fair do's I suppose. it just gets confusing when even your own lecturer's notes are switching between the terms...

[phyzguy]

Tell me about it. I used to have a professor who would ask, "What did I call this the last time?"

[Mindscrape]

They all mean the same thing, they are all talking about a ket. I find that typically people will say eigenstate and eigenfunction when talking about a general ket, eigenfunction if they have a particular wave function, and they say eigenvector when the ket is in a matrix form (such as spinors).

It's kind of like how in differential equations you would solve the characteristic equation, and people would say, oh you found the eigenvalues. And at the time you were like, eigenvalues, huh, I never used any matrices. Then later you learned that, oh the system can be represented in another way, and I really have been solving for eigenvalues.