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Completeness of Eigenfunctions

  1. May 11, 2009 #1
    1. The problem statement, all variables and given/known data

    What is meant by the completeness of eigenfunctions?


    3. 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?
     
  2. jcsd
  3. May 11, 2009 #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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