Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many noninteracting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the leading corrections to Thomas-Fermi theory, involve neither sums nor derivatives, are spatially uniform approximations, and are exceedingly accurate.

The aim of this paper is to introduce a new approximate method, namely the Modified Laplace Padé Decomposition Method (MLPDM) which is a combination of modified Laplace decomposition and Padé approximation to provide an analytical approximate solution to Thomas-Fermi equation. This new iteration approach provides us with a convenient way to approximate solution. A good agreement between the obt...

We study a system of $ N trapped bosons in the Thomas-Fermi regime with an interacting pair potential form g_N N^{3\beta-1} V(N^\beta x) $, for some \beta\in(0,1/3) and diverging as \to \infty $. prove that there is complete Bose-Einstein condensation at level ground state and, furthermore, that, if \beta\in (0,1/6) preserved by time evolution.