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 Jul30 revised FFT for solving Poisson equation in 3 dimensions with periodic boundary conditions clearer text Jul30 revised FFT for solving Poisson equation in 3 dimensions with periodic boundary conditions improved english Jul30 accepted FFT for solving Poisson equation in 3 dimensions with periodic boundary conditions Jul2 awarded Curious Oct21 awarded Tumbleweed Oct1 awarded Critic Oct1 answered Taylor expansion of functional Sep19 awarded Popular Question Jul15 asked To calculate a derivative of a set of points, is it more correct to interpolate finite differences or to derivate the interpolation? Feb6 revised Laplace transform of the square root of a generic function introduction of a special case, and no assumption about existence of the transform. Feb5 asked Laplace transform of the square root of a generic function Jan11 comment FFT for solving Poisson equation in 3 dimensions with periodic boundary conditions That's very nice I'll now be able to demonstrate the Froueri transform (whatever the definition) of $\Delta$. Thank you @Fabian. What is unclear to me is considering my practical problem and the actual definition of backward FFT in FFTW, what should I divide the forward FFT of $-\rho(\mathbf{r})/\epsilon_0$ by in order to calculate $V(\mathbf{r})$? Jan11 comment FFT for solving Poisson equation in 3 dimensions with periodic boundary conditions @Fabian corrected. Thanks. Jan11 revised FFT for solving Poisson equation in 3 dimensions with periodic boundary conditions Corrected expression of $\Delta V$ in kspace. Thanks @Fabian Jan11 asked FFT for solving Poisson equation in 3 dimensions with periodic boundary conditions Jul23 comment integral of a spherically symmetric 3-dimensional function over all space As I told before ... I'm not used to deal with mathematics but I'm hunger to learn. Thanks @joriki and J.M. for your remarks. Here is the point about the values near $\vec{r}-\vec{r}'=0$: the LJ potential is also modified at small $r$, for instance using the Weeks-Chandler-Andersen scheme (this question is related to our study of perturbation theory for hard spheres thermodynamics) Jul23 accepted integral of a spherically symmetric 3-dimensional function over all space Jul23 comment integral of a spherically symmetric 3-dimensional function over all space @Joriki: thanks a lot for this very clear explanation. In order to answer your very last sentence "small wonder that you've divergence": I use pair potential that converges to zero at a non-infinite radius. In fact, when people in my community say LJ potential, they mean troncated LJ potential. Sorry for the misunderstanding I should have been more careful. Thanks again I am very happy with your answer. Jul22 revised integral of a spherically symmetric 3-dimensional function over all space Changed the text in order to make clearer where my question is. Jul22 comment integral of a spherically symmetric 3-dimensional function over all space Sorry if the question was unclear: I wanted to ask if my last equation line is right (going from spherical to radial integration for a spherically symmetric function $u$). What $u$ is isn't important as this integration will be done numerically for any kind of $u$ (it's a two centers interaction potential let's say a Lennard Jones 6-12 for instance). Thank you Joriki et al! @Alice: Hi! it is indeed very linked in the sens that now that I understand this, I can understand your demonstration for my other question! Once more thank your!