Solution of the Thomas-Fermi-Dirac Equation

A Z-dependent variational solution of Thomas-Fermi-Dirac equation

Using Thomas-Fermi-Dirac equation within the exchange-correlation scheme and a Z-dependent trial solution, the ground state binding energy for neutral, positively, and negatively charged atoms are calculated. Comparing to the results obtained in earlier works, the values of the binding energy estimated here for both light and heavy atoms agree nicely with the Hartree-Fock values. We have also c...

Dipole Moments in Thomas-Fermi-Dirac and Thomas-Fermi Theories

An explicit analytic solution to the Thomas-Fermi equation

In this paper, a newly proposed analytical scheme by the authors namely the improved di erential transform method is employed to provide an explicit series solution to the Thomas Fermi equation. The solution procedure is very straightforward, requiring merely elementary operations together with di erentiation, and ends up in a recursive formula involving the Adomian polynomials to a ord the unk...

Variational approach to the Thomas-Fermi equation

By the semi-inverse method, a variational principle is obtained for the Thomas– Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method. 2002 Elsevier Science Inc. All rights reserved.

Rational approximation to the Thomas–Fermi equation

We discuss a recently proposed analytic solution to the Thomas– Fermi (TF) equation and show that earlier approaches provide more accurate results. In particular, we show that a simple and straightforward rational approximation to the TF equation yields the slope at origin with unprecedented accuracy, as well as remarkable values of the TF function and its first derivative for other coordinate ...