Re: [Wavepacket-user] Coulomb problem

[Lorenz, U. <ulf...@de...>]

One correction , and one addon:


> On Wed, 2010-10-20 at 17:38 +0800, wanglei365x wrote:
> > Hello,
> > 
> > I am trying to solve the  hydrogenlike Coulomb problem in Fourier
> > method. The wave function has the boundary condition fai(0)=0. So i
> > have to double the grid over to the negative r side.  When implement
> > the 'wavepacket', in this r range, the grid_fft grid contain a grid
> > point 'r_i = 0', this make the Coulomb potential divergence. And the
> > choice  of value of the variable 'hamilt.truncate' makes significant
> > influence to the result. Is this problem existence in the 'wavepacket'
> > and how can i set the value of the variable 'hamilt.truncate'(the
> > estimate Coulomb potential is divergence near the origin)

I have not quite understood which problem you solve how: Do you have the
3D Coulomb problem after separating the angular coordinates (which would
leave you with an effective 1D Coulomb problem)?

> You can use a soft Coulomb potential, i.e., replace V(r) = 1/r^2 by
> something like V(r) = 1/(r^2 + a^2), which provides a smoother
> truncation than just setting hamilt.truncate to some value.

The Coulomb potential is of course 1/r, and the soft potential was probably
1/sqrt(r^2 + a^2) for some constant a.


Ulf