# Majorana solution of the Thomas–Fermi equation

@article{Esposito2001MajoranaSO, title={Majorana solution of the Thomas–Fermi equation}, author={Salvatore Esposito}, journal={American Journal of Physics}, year={2001}, volume={70}, pages={852-856} }

We report on an original method, due to Majorana, that leads to a semi-analytical series solution of the Thomas–Fermi equation with appropriate boundary conditions in terms of only one quadrature. We also deduce a general formula for such a solution that avoids numerical integration, but is expressed in terms of the roots of a polynomial equation.

## 60 Citations

### On the Majorana solution to the Thomas-Fermi equation

- MathematicsArXiv
- 2021

We analyse the solution to the Thomas-Fermi equation discovered by Majorana. We show that the series for the slope at origin enables one to obtain results of accuracy far beyond those provided by…

### Analytical approximate solutions to the Thomas-Fermi equation

- Mathematics
- 2014

The purpose of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to solve the nonlinear differential Thomas-Fermi equation. Our procedure does not depend upon small…

### Accurate calculation of the solutions to the Thomas-Fermi equations

- PhysicsAppl. Math. Comput.
- 2014

### Majorana Transformation for Differential Equations

- Mathematics
- 2002

We present a method for reducing the order of ordinary differential equations satisfying a given scaling relation (Majorana scale-invariant equations). We also develop a variant of this method, aimed…

### Numerical Solution of the Thomas–Fermi Equation for the Centrally Symmetric Atom

- Physics
- 2004

The computational aspects are analyzed of the Thomas–Fermi equation for a spherically symmetric and electrically neutral atom of finite size that is part of a solid. The limits are identified of the…

### Fractional order of rational Jacobi functions for solving the non-linear singular Thomas-Fermi equation

- Mathematics
- 2017

Abstract.In this paper, a new method based on Fractional order of Rational Jacobi (FRJ) functions is proposed that utilizes quasilinearization method to solve non-linear singular Thomas-Fermi…

### Analytical-Numerical Method for Calculating the Thomas-Fermi Potential

- PhysicsRussian Journal of Mathematical Physics
- 2019

A method for computing the solution to the boundary value problem for the symmetric Thomas-Fermi model of a heavy atom or ion at zero absolute temperature.

### A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions

- Mathematics
- 2016

In this paper, the fractional order of rational Bessel functions collocation method (FRBC) to solve Thomas-Fermi equation which is defined in the semi-infinite domain and has singularity at $x = 0$…

### Generalized Thomas–Fermi equations as the Lampariello class of Emden–Fowler equations

- Mathematics
- 2016

### A novel numerical technique to obtain an accurate solution to the Thomas-Fermi equation

- Mathematics
- 2016

Abstract.In this paper, a new algorithm based on the fractional order of rational Euler functions (FRE) is introduced to study the Thomas-Fermi (TF) model which is a nonlinear singular ordinary…

## References

SHOWING 1-10 OF 13 REFERENCES

### Pedagogic notes on Thomas-Fermi theory (and on some improvements): atoms, stars, and the stability of bulk matter

- Physics
- 1991

In the more than half century since the semiclassical Thomas-Fermi theory of the atom was introduced, there have been literally thousands of publications based on that theory; they encompass a broad…

### The calculation of atomic fields

- PhysicsMathematical Proceedings of the Cambridge Philosophical Society
- 1927

The theoretical calculation of observable atomic constants is often only possible if the effective electric field inside the atom is known. Some fields have been calculated to fit observed data but…

### Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente

- Physics
- 1928

ZusammenfassungBei einem schweren Atom können die Elektronen als eine Art Atmosphäre um den Kern betrachtet werden, welche sich in einem Zustand vollständiger Entartung befindet. Man kann die…

### Physics of atoms and molecules

- Physics, Chemistry
- 1982

1. Electrons, photons and atoms. 2. The elements of quantum mechanics. 3. One-electron atoms. 4. Interaction of one-electron atoms with electromagnetic radiation. 5. One-electron atoms: fine…

### Black Holes, White Dwarfs, and Neutron Stars

- Physics
- 1983

Only for you today! Discover your favourite black holes white dwarfs and neutron stars book right here by downloading and getting the soft file of the book. This is not your time to traditionally go…

### Am. J. Phys

- Am. J. Phys
- 2002

### Integrazione asintotica dell ’ equazione differenziale Thomas – Fermi

- R . Accademia dei Lincei
- 1983

### Ettore Majorana: Notebooks in Theoretical Physics ͑Kluwer

- Ettore Majorana: Notebooks in Theoretical Physics ͑Kluwer

### Self-Consistent Fields in Atoms ͑Pergamon

- Physics of Atoms and Molecules ͑Longman
- 1975