What is the difference between Eigenstate and Eigenfunction??

Question

michele_laino · Answer

The eigenstate is a state, and the eigenvalue is its corresponding value, namely the number which express the result of a measure made on our system

anonymous · Answer

Eigenstate is a state and Eigenfunction is function. Just like you replied to my question huh!!!!!!!

anonymous · Answer

@Gopz.. ha ha..

@michele.. eigenfunction and eigenstate??

anonymous · Answer

Maybe in principle, not really in practice. Most people talking casually will use the interchangeably.

If you want a rule that makes sense though, "states" are what we call the objects that live in a hilbert space (we also call them vectors, thus eigenvectors!) so the generic, "coordinate-independent" ket should be the eigenstate.

It's projection onto a definite coordinate basis (say space or momentum) then becomes a mathematical function of that coordinate, so we should call that guy the eigenfunction (which then becomes a basis dependent notion)

michele_laino · Answer

oops.. sorry @Angu 
eigenstate is a vector, whereas an eigenfunction is a function evalued on some eigenvalues which belong to some eigenstates