I am studying the Scattering theory by John R. Taylor but I met a mathematic problem in Section 11-h.
$\phi_{lp}(r)$ is the solution of radial Schoedinger equation:
$$ \Big[\frac{d^2}{dr^2}-\frac{l(l+1)}{r^2}+p^2\Big]\phi_{lp}(r)=U(r)\phi_{lp}(r) $$
with the boundary condition: $\phi_{lp}(0)=0.$ The corresponding Green's function is:
$$ \Big[\frac{d^2}{dr^2}-\frac{l(l+1)}{r^2}+p^2\Big]g_{lp}(r,r')=\delta(r-r') $$
The particular solution is: $$\phi_{lp}(r)=\int dr'g_{lp}(r,r')U(r')\phi_{lp}(r')$$
The boundary condition of Green's function is also: $g_{lp}(0,r')=0.$ How can I solve out this Green's function?