# Finding Greens Function using the delta function

I have the linear differential operator $$Lu = u''-(1+x^2)u = f(x)$$ with BCs s.t. $u$ vanishes at positive and negative infinity. The hint I was given is to show that $u_0=e^{-x^2/2}$ satisfies $Lu_0=0$ and then find greens function of the form $wu_0$. I have tried this and end up with the $erf$ function as I need to integrate $e^{-t^2}$, this doesn't seem quite right so just wondering if anyone has any tips? Thanks!

• Please show the details of your solution and the result you obtained – Yuriy S Feb 8 '18 at 15:08
• So I tried to solve $Lg=\delta(x-\xi)$, where $g=wu_0$ along with the boundary conditions and after some calculation I ended up with $w=\int^xAe^{-t^2}dt$ but then things get messy after I try and work out the constants using the BCs and continuity – Deke Feb 8 '18 at 15:12