An analytic solution to the Thomas–Fermi equation

Abstract

A perturbative procedure due to Bender e t a l. (here referred to as the BMPS procedure) [J. Math. Phys. 3 0, 1447 (1989)] and useful in solving difficult nonlinear problems, has been used here to solve the Thomas–Fermi (T–F) equation. The present work attempts to balance the ease of the ensuing analysis with the use of an analytic, zero‐order function that already contains a good deal of the nonlinearity of the T–F equation. The initial slope of the T–F potential is computed with 0.35% error in a second‐order application of the theory.