Systematization of the Approximate Solutions of the Thomas-Fermi Equation

Abstract

Based on the generalized Brinkman's remark that x σ φ can be treated as a constant over the whole range of x , three homologues of the approximate TF solutions, i.e. 1. Brinkman, 2. Kerner-Tietz-Umeda and 3. Sommerfeld-March, are systematically established under either of two different guiding principles, the linearization of the TF equation in regard to φ and the elimination of the explicit x in the TF equation.