I can not understand one simple thing dealing with Fourier
transformation.
May be somebody explain me.

I consider two-dimension lattice of the electrical charges bathed by
electrolyte.
The electric potential in each lattice site due to all others charges
is

Psi = const *Sum {Exp[-kapa*R(i,j)] / R(i,j)} (1)

(kapa is invert Debye’s length; R(i,j) is the separation between
selected site and charge located in (i,j)-site)

There is not divergence in (1) due to screening. One can calculate Psi
from (1) for any non-zero kappa.

Let us now rewrite (1) using common Fourier transformation of lattice
charge distribution. Then Psi becomes


Psi = const *Sum {1/ Sqrt[kapa^2+k^2]} (2)

Here k is determined by invert lattice constant, which is connected
with real lattice constant “a” as k^2=(6.28/a)(m^2+n^2)



Eq.(1) and (2) have to be the same. But Eq.(1) give certain finite Psi
at the same time sum in Eq.(2) diverges and Psi from (2) go to
infinity for any finite kappa.

Where do I mistake?


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