DERIVATION OF THE DIMENSIONAL THOMAS-FERMI EQUATION FOR THE THOMAS-FERMI ATOM MODEL

Abstract

This article presents a method for calculating the energies of the values of the set of electron-neutral atoms. In this case, the interaction of electrons other than the Coulomb bond of the nucleus makes an important contribution to energy. Quantitative calculation of the interaction of these interactions with the introduction of the theory of approximation in the framework of the Thomas-Fermi statistical model by the method of self-correction field is particularly inefficient for complex atoms. However, for complex atoms, the method of approximation is shown, and its essence lies in its simplicity. Among the various methods for systems consisting of the same number of particles, the statistical method derived from the Thomas-Fermi statistical model of the atom plays an important role. This method (E. Fermi, L. Thomas, 1927) is based on the fact that in complex atoms with a large number of electrons, most electrons have relatively large quantum numbers. In this case, a semi-classical approximation is used. As a result, the concept of "cells in phase space" can be used for the state of the individual electrons of the atom. This model has been developed by researchers over a long period of time and has led to a consistent, complete doctrine without the defects of previous models, for example, its field of application is wider than the original Thomas-Fermi.