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I want to solve this eq. (k(x)*g(x)')'=p*g(x)

  1. Mar 9, 2010 #1
    I have the following equation:


    k(x) = k(x+T) -- k(x) is a known periodical function of period T, k(x) real, x real, T real.
    p = some constant that have to be determined.
    g(x) = an unknown function.

    Question: Is there a method that can tell from the beginning that all the values of p should be real?

    If p is always real I will try to solve the equation if p could also be complex the equation will not be of so much interest for me.
  2. jcsd
  3. Mar 10, 2010 #2
    Can somebody prove that the operator:

    H = d/dx(k(x)*d/dx) corresponding to the above mentioned equation, Hg(x)=p*g(x), is hermitian?

    I understand that if you prove this then all the values of p must be real.
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