Asymptotics of solutions of a generalized Thomas-Fermi equation

Regularly Varying Solutions of Generalized Thomas-fermi Equations

Quantum Mechanics as Asymptotics of Solutions of Generalized Kramers Equation

We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this model, the usual quantum description arises as asymptotics of this process for large values of resistance of the medium per unit of mass of particle. It is ...

Existence of positive solutions for a generalized and fractional ordered Thomas-Fermi theory of neutral atoms

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 ...