Re: [Wavepacket-user] Coulomb problem

[Ulf L. <ulf...@de...>]

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)

It is a while ago that I have last seen the Coulomb problem, but as far
as I remember, there are two approaches.

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. This
potential has AFAIR a few properties that were different from the raw
Coulomb potential, but I do not recall which. I also remember that this
was sort of the standard first approach one often sees in strong-field
ionization.

I also remember having seen also something called scaled Fourier method
or so that was said to be useful for the raw Coulomb problem, but I have
no idea where. Probably one of the Big Guys (e.g., Kosloff, Tannor) has
published something in this direction, and it is on my eternal list of
things to look up one day. In any case, this method is not implemented
in WavePacket.


Does this help?

Ulf