What is meant by the completeness of eigenfunctions?

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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?
 

Answers and Replies

  • #2
HallsofIvy
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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.
 

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