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!

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

Can you offer guidance or do you also need help?



Similar Discussions: ODE with delta functions
Loading...