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From: Lorenz, Ulf <ulf.lorenz@de...>  20101024 18:55:56

One correction , and one addon: > On Wed, 20101020 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 
From: Ulf Lorenz <ulf.lorenz@de...>  20101021 09:26:06

On Wed, 20101020 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 strongfield 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 
From: wanglei365x<wanglei365x@16...>  20101020 09:38:34

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) 20101020 wanglei365x 
From: Ulf Lorenz <ulf.lorenz@de...>  20101020 07:57:00

On Wed, 20101020 at 10:35 +0800, wanglei365x wrote: > hello, > i am one of the wavepacketusers, i am confusing about the following > questions: Great, feedback. :) > what does the variable 'hamilt.truncate' mean, why we need it, and how > to decide it? The variable used to be more central, and is admittedly hard to follow in the code flow. However, it still has two uses: 1. Less important: When plotting, in the absence of other parameters, it is used to select some energy ranges for the plot. However, there are other variables nowadays, which are not really documented and sometimes do the same (making developing note). 2. For the Chebychev propagator to converge, all eigenvalues of the Hamiltonian must be in a finite range [min,max]. Furthermore, the propagator is faster (allows larger time steps with the same accuracy and cost) the smaller the range delta = maxmin is. In this case, hamilt.truncate.{minmax} is used to truncate the potential and kinetic energy grids so that they are guaranteed to have eigenvalues in the range [min,max] (potentials) or [0,delta] (kinetic energy). Then the bounds are added to give a worst case estimate of the smallest and largest eigenvalue of the total Hamiltonian (stored in hamilt.{min max}), which you can override if you know better. If you normally use the split operator and do not care too much about the plots (or fiddle around with them using plots.pot.{minmax}) then you can ignore this variable. If you set it, set it such that the important part of the potential and kinetic energy is safely within the boundaries. Ulf 
From: wanglei365x<wanglei365x@16...>  20101020 02:36:09

hello, i am one of the wavepacketusers, i am confusing about the following questions: what does the variable 'hamilt.truncate' mean, why we need it, and how to decide it? i am looking forward your reply. 20101020 wanglei365x 