What is the difference between eigenfunctions and eigenvectors?

[Amith2006]

In Quantum mechanics, we frequently deal with eigen value equations. When we speak of eigen value equations, we come across terms like eigen values,eigen vectors,eigen functions etc. When an operator is operated on certain quantities we get the same quantity multiplied by a constant. These quantities are interchangeably referred as eigen vectors and eigen functions. But do they mean the same? Is it something like, we call it as eigenfunctions in Schrödinger formalism and eigenvectors or eigenkets in Heisenberg formalism or is there a ma thematical difference between the 2?

 

[Fredrik]

They are the same. It would be weird to use "eigenket" when you're not using bra-ket notation, and it would be weird to use "eigenfunction" if you're talking about a vector that isn't actually a function, but other than that they're the same. The term "eigenstate" is also used interchangeably with the others. That's actually a little bit weird since a "state" is represented by an equivalence class of vectors. (Two vectors are equivalent if one of them is a complex number times the other).