Analysis of Thomas-Fermi Energy Functional Under Two Potentials
Keywords:
Thomas-Fermi theory, Sobolev-Lieb inequality, Density functional method, Free-Energy functional, Functional derivative, Density matrixAbstract
In this paper, by constructing Free-energy Functionals, the Thomas-Fermi theory has been extended to include the non-zero temperature effects in many-particle systems. Using the Sobolev-Lieb and the Hőlder inequalities, the constructed Free-energy Functionals were put into a form from which an extended Thomas-Fermi equation was derived. Hitherto, in this work, the two states Ψ0(r) and Ψ1(r), corresponding respectively to the square root of two densities r0(r) and r1(r), had been used to construct the new free-energy Functionals F[r0(r)] and F[r1(r)]. The states Ψ0(r) and Ψ1(r) were required to be mutually orthogonal, and the functional F[r0(r)] was considered as the ground state functional while F[r1(r)] was the excited state functional with temperature 0. From the functionals, the electron density matrix was derived and finally the total energy was computed for many-electrons system under the influence of the Coulomb and Yukawa Potentials. Various results were obtained and discussed.
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