ODE with delta functions

1. Jul 17, 2012

Combinatorics

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

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$r=0$ to this situation...