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November 24th, 2016, 02:15 AM   #1
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POTENTIAL: sum ∑ to integral

Hi, I'm new to this forum.
I have a task to do: positive charged particle (proton in this case) is traversing throught channel in crystal lattice ((100) direction in FCC crystal for example). But in my case thing is little more simple: positive particle i passing near row (string) of atoms that are all on same spacing "d".
123.jpg
Total potential is sum of all potentials from every single atom in row:
U(total) = ∑ Ui(Ri),
where Ri is distance from positive particle to i-th atom in row. So sum goes from first particle in row to last particle in row, and "i" is number of particles in row.
How come that this sum can be changed with integral?
Integral is:
111.jpg
What is procedure, step by step for this equation?
Thank You,
Nikola
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November 24th, 2016, 10:40 AM   #2
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