Of course numerical techniques won't give an expression for eigenfunction, but I am looking for a vector of values of the eigenfunction in a given range. Also, do Scilab or Octave have any built-in functions for finding them?
For instance, I was trying to solve the Schrodinger equation for the hydrogen atom and I ended up with the following eigenvalue equation,
with the initial condition that
$\psi(0.0001)=0.0001$ and $\psi'(0.0001)=1$
I am starting a bit away from origin because, I have $r$ in the denominator. I just want to find the eigenvalues and plot it's eigenfunctions.