Thomas-Fermi Screening in One Dimension

The Thomas-Fermi method has been applied to the problem of screening due to an electron gas confined to a filament and a coaxial infinite cylinder. Using parameters derived for ${\mathrm{K}}_2$Pt${\mathrm{}\left(\mathrm{CN}\right)\mathrm{}}_4$ ${\mathrm{Cl}}_{0.32}$·2.6${\mathrm{H}}_2$0, the potential in the region between the filament and cylinder due to a source charge in the filament was evaluated and was found to vary approximately as $\frac{e^{-k_{\mathrm{eff}}\mathcal{r}}}{\mathcal{r}}$ with an effective screening length about ten times that of metallic platinum. The isotropic form of the screened potential shows the close relationship to screening in three dimensions.