What is meant by the completeness of eigenfunctions?

[dave4000]

Homework Statement

What is meant by the completeness of eigenfunctions?

The Attempt at a Solution

I understand the AX(x)=BX(x) where A is the operator, B is the eigenvalue and X(x) the eigenfunction.

I cannot find anywhere anything on what is meant by the completeness of eigenfunctions. Any idea?

 

[HallsofIvy]

A "complete" set of eigenvectors (called eigenfunctions if you vector space is a space of functions) is a set of eigenvectors that forms a basis for the vector space. In particular, "self adjoint" operators always have a complete set of eigenvectors.