I've been looking into radial solvers for quantum wave equations (Schroedinger and Dirac). In both cases, the suggestion seems to be to go with the "shooting method", with integration schemes of various precision such as the Numerov one.

Now, for a shooting method, one needs to impose starting values coming from boundary conditions. Many texts mention asymptotic behaviours such as Bessel functions near $r=0$ etc. Since my interest is in solving perturbed versions of the basic Coulomb potential, and the solution for this problem is already known, however, couldn't I just start with the known hydrogen-like solution and work from there? Or is there some reason why this is not indicated?


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