I have a problem that I've been unable to find a simple solution for.(adsbygoogle = window.adsbygoogle || []).push({});

When solving Schroedinger's equation for a central force, the nonradial part of the solution can be found with spherical harmonics, but the radial part is much more difficult.

[itex]E\psi = - \frac{1}{2m}\left(\frac{d^2\psi}{dr^2} + \frac{2}{r}\frac{d\psi}{dr} - \frac{l(l+1)}{r^2}\psi\right) + V(r)\psi[/itex]

E = energy, V = potential, m = mass, [itex]\psi[/itex] is the field variable.

The problem is the coordinate singularity at the origin.

For zero angular momentum [itex]l[/itex], one can solve for [itex]r\psi[/itex], and one gets an equation without a coordinate singularity. One can easily finite-difference it and then solve it as an eigensystem.

But for nonzero angular momentum, that coordinate singularity cannot be eliminated by this means. Is there some alternative way of handling that coordinate singularity in this case?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Finite-Difference Solutions of Radial Equations: Handling the Origin for D > 1?

Loading...

Similar Threads for Finite Difference Solutions |
---|

A Runge Kutta finite difference of differential equations |

A Convergence order of central finite difference scheme |

A Finite Difference |

A Better way to find Finite Difference |

**Physics Forums | Science Articles, Homework Help, Discussion**