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Homework Help: Is 0 ever an eigenfunction?

  1. Jun 8, 2007 #1
    1. The problem statement, all variables and given/known data
    If y(x)=0 satisfies the ode and all the boundary conditions than does it count as the first eigenfunction?

    3. The attempt at a solution
    It wouldn't satisfy the orthogonality relation though? In that the integral of 0 and 0 is 0 even though the integral is over two eigenfunctions that are the same.
     
  2. jcsd
  3. Jun 8, 2007 #2

    Dick

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    A linear operator acting on the zero vector is always the zero vector. This doesn't count as 'eigen' behavior. Otherwise every linear operator would have zero eigenvalue. Read a carefully stated definition of eigenfunction.
     
  4. Jun 8, 2007 #3
    Good point. I should always relate to linear algebra. The 0 vector is never an eigenvector as it would imply the determinant of the matrix is nonzero.

    So the 0 function is never the eigenfunction.
     
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