» Esercizi svolti di Matematica e Fisica

That damned equation (Thomas-Fermi equation)

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.

Subjects:

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

• A boundary problem
• A boundary problem
• Complete solution

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