Screened Coulomb potential for a quantum wire in the Thomas-Fermi approximation

We derive the dielectric function and screened Coulomb potential of a quantum wire by using a one-dimensional (1D) generalization of the Thomas-Fermi approximation (TFA). To apply the TFA approach to all temperatures we employ a constructive method based on the standard Padé approximant technique to approximate the dependence of the temperature of the 1D TFA parameter $q_s{=2e}^2\partial n/\partial \mu .$