Related papers: Accurate calculation of the solutions to the Thoma…
We show that a simple and straightforward rational approximation to the Thomas-Fermi equation provides the slope at origin with unprecedented accuracy and that relatively small Pad\'e approximants are far more accurate than more elaborate…
An approximate analytical solution of the Thomas-Fermi equation for neutral atoms is obtained, using the Ritz variational method, which reproduces accurately the numerical solution, in the range $0\leq x\leq50$, and its derivative at $x=0$.…
It is well known that the ultra-relativistic Thomas-Fermi equation, amply adopted in the study of heavy nuclei, admits an exact solution for a constant proton distribution within a spherical core of radius Rc. Here exact solutions of a…
The Thomas - Fermi equation describing the screening of the Coulomb potential inside heavy neutral atoms is reconsidered. An accurate representation for its numerical solution was obtained by means of the variational principle. The proposed…
In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system…
We propose a method for the treatment of two--point boundary value problems given by nonlinear ordinary differential equations. The approach leads to sequences of roots of Hankel determinants that converge rapidly towards the unknown…
In this paper, we consider the numerical solution of highly-oscillatory Vlasov and Vlasov-Poisson equations with non-homogeneous magnetic field. Designed in the spirit of recent uniformly accurate methods, our schemes remain insensitive to…
Stochastic solutions are obtained for the Maxwell-Vlasov equation in the approximation where magnetic field fluctuations are neglected and the electrostatic potential is used to compute the electric field. This is a reasonable approximation…
We construct two rational approximate solutions to the Thomas-Fermi (TF) nonlinear differential equation. These expressions follow from an application of the principle of dynamic consistency. In addition to examining differences in the…
Present day electromagnetic field calculations have limitations that are due to techniques employing edge-based discretization methods. While these vector finite element methods solve the issues of tangential continuity of fields and the…
Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many non-interacting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the…
The explicit analytic solution of the Thomas Fermi equation thorough a new kind of analytic technique, namely the homotopy analysis method, was employed by Liao (Appl. Math. Comp. 144, (2003)). However, the base functions and the auxiliary…
We discuss the exact polynomial solutions for the two-dimensional hydrogen atom in a constant magnetic field already studied earlier by other authors. In order to provide a suitable meaning for such solutions we compare them with numerical…
We present a new pseudospectral algorithm for the calculation of the structure of atoms in strong magnetic fields. We have verified this technique for one, two and three-electron atoms in zero magnetic fields against laboratory results and…
Fully numerical mesh solutions of 2D and 3D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of…
The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon…
With the use of the general covariant matrix 10-dimensional Petiau-Duffin-Kemmer formalism in cylindrical coordinates exact solutions of the quantum-mechanical equation for a particle with spin 1 in the presence of an external homogeneous…
The Thomas-Fermi approximation for an atomic wavefunction is used to calculate the interaction of a neutron spin with the atomic electric field, either through motional magnetic (v x E) or possibly electric (due to the possible existence of…
In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it is needed to consider the effect of external…
In this paper we develop a numerical method for efficiently approximating solutions of certain Zakai equations in high dimensions. The key idea is to transform a given Zakai SPDE into a PDE with random coefficients. We show that under…