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Homework Help: ODE with delta functions

  1. Jul 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Find negative eigenvalues and corresponding eigenfunctions to the following operator:
    [itex] H:= - \frac{d^2}{dx^2} - \delta_{-r} -2\delta{r} [/itex] .
    (The eigenfunction should be twice contiously differentiable, except for possible jump discontinuities at [itex] +-r [/itex] of the first and second derivatives. In addition, the eigenfunctions [itex]f[/itex], must satisfy that [itex]f, f' , f'' = O(1/|x|) [/itex]

    2. Relevant equations
    3. The attempt at a solution

    I really have no idea about it... I found this question on the web-
    http://www.harding.edu/lmurray/Quantum_files/_Ch5 Delta Function Potential.pdf
    (problem 5.1)
    and I can't figure out how to generalize the calculation for[itex] r=0 [/itex] to this situation...

    Your help is needed!

    Thanks !
  2. jcsd
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