ABSTRACT
The Thomas-Fermi Equation (TFE) is a nonlinear, second-order differential equation for which no exact general solution is known to exist in terms of a finite combination of the elementary functions. As a consequence and because of its importance for atomic physics, hundreds of research papers have been published on the construction of analytical approximations to its solutions. The main purpose of the current presentation is to use a new methodology to construct such approximate solutions. Dynamic consistency (DC) is a principle that allows people to assess the “closeness” or “fidelity” of two systems based on their mutually shared properties. The exact solution to the TFE is unknown. A word of caution should now be given regarding approximations to the solution of the TFE. The TFE is based on a number of both physical and mathematical assumptions.
