Abstract
In this paper, we point out that the problem of a system of many particles can be simplified into that of a single electron by using Thomas-Fermi potential in Raman free-electron lasers. Klein-Gordon equation is solved by using perturbation theory. The formula of the density of electric charge and current density are derived from the corresponding zero order wave function. If we simplify properly the Klein-Gordon equation, we can solved by using the methods of seperation of variables and WKB approximation. We also derived the formula of the electric charge and current density which correspond to the new wave function.
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