1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Is 0 ever an eigenfunction?
Loading...