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Solve the eigenvalue problem

  1. Oct 14, 2007 #1
    Solve the eigenvalue problem O[tex]_{6}[/tex] [tex]\Psi[/tex](x) = [tex]\lambda[/tex] [tex]\Psi[/tex](x)

    O[tex]_{6}[/tex][tex]\Psi[/tex](x) = [tex]\int[/tex] from negative infinity to x of dxprime *[tex]\Psi[/tex](xprime) * xprime
    what values of eigenvalue [tex]\lambda[/tex] lead to square integral eigenfuctions? (Hint: Differentiate both sides of the equation with respect to x)

    Im trying to do this with integration by parts but i keep getting infinity in some form or another. Im assuming [tex]\Psi[/tex](xprime) is equal to the derivative of [tex]\Psi[/tex](x) with respect to x. so i end up with [tex]\lambda[/tex][tex]\Psi[/tex](xprime) is equal to some integral that keeps working out to infinity. I dont want anyone to give me a solution but if anyone can give me a bump in the right direction i would be pumped.

  2. jcsd
  3. Oct 14, 2007 #2


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    You aren't paying enough attention to the hint. How do you find d/dx of an integral with x as the upper limit? You should get a simple ODE to solve for psi.
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