I wish to solve an eigenvalue problem:
If I assume spherical symmetry $f(r,\theta,\phi)=f(r)$, I can reduce the problem to 1D:
My boundary conditions are $f(r=0)=0$ and $f(r=L)=0$, where $L$ is the size of the discrete grid.
I am attempting to solve this problem using a orthogonal basis set expansion, but the issue I am experiencing is the divergence of $r$ at $r=0$. Is there a better method for solving this type of problem? How can I accommodate the singularity?