That Damned Equation – The Thomas–Fermi

The Italian physicist Ettore Majorana mysteriously disappeared in 1938. Majorana was part of the famous Via Panisperna group directed by Enrico Fermi. In those years the model of «heavy atom» (that is, with many electrons) was proposed, and Fermi elaborated a model based on Statistical Quantum Mechanics known as the Thomas-Fermi model (as established in the same period by Llewellyn Thomas). This model was governed by a nonlinear second-order differential equation. Numerical integration was extremely complicated. Fermi and his group had been working on it for a week. Ettore Majorana only needed one night’s work not only to integrate the equation, but to develop a sophisticated algorithm for the solution of an entire class of differential equations. In the ebook that we offer today we present our solution obtained with the aid of the Mathematica software.


Genesis of the Thomas – Fermi equation
Historical note
A particular integral of the Thomas-Fermi equation

A boundary problem
A boundary problem
Complete solution

Marcello Colozzo, a graduate in Physics, has been involved in online teaching of Mathematics and Physics since 2008 through the Extra Byte website where “simulations” are performed in the Mathematica computing environment. In recent years he has published various articles on mathematical physics and collaborates with the Electronic Open Source magazine. An avid reader of cyberpunk fiction, he has attempted to transition into “cyber writer” status by publishing various anthologies of short stories.

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