Fermi passed an examination

In the spring of 1927 Orso Mario Corbino, the director of the Institute of Physics at Rome and an influential politician, launched a famous appeal to the students of the Faculty of Engineering to entice the most brilliant young minds into studying Physics. Segrè and his friend Amaldi rose to the challenge, joining Fermi and Franco Rasetti’s group and telling them of Ettore’s exceptional gifts. After some encouragement from Segrè and Amaldi, Majorana eventually decided to meet Fermi in the autumn of that year. The pair immediately started talking about the statistical model of atoms that Fermi was working on, later to be known as the Thomas–Fermi model, which describes the energy of an atom in terms of the density of its surrounding electrons. The model involves a complicated non-linear differential equation. The analytical solution of the equation was then unknown, but Fermi had managed to obtain a numerical table of approximate values for it. Majorana carefully followed what Fermi said and, after asking a few questions, left the Institute. The following morning he returned to Fermi’s office and asked for a closer look at the numerical table so that he could compare it with an analogous table he had drawn up the previous evening. Once he had established agreement between the two tables, Majorana noted that Fermi’s table was correct and left the Institute with no further comment.

What seems nothing more than an amusing anecdote, as recalled by Rasetti, Segrè and Amaldi, has since been carefully tested on scientific grounds. From previously unpublished study notes written by Majorana between 1927 and 1932, we now know that Majorana had arrived at a “series solution” of the Thomas– Fermi equation using a peculiar method that applies to an entire class of mathematical problems. It is testament to Majorana’s genius that although some of his results anticipated by several years those of renowned mathematicians and physicists, several others (including his solution of the Thomas–Fermi equation) have not been obtained by anyone else since.

As if satisfied that Fermi had passed his “examination”, Majorana decided to leave engineering and join what became known as the “via Panisperna boys” – Fermi’s influential group that was named after the street in Rome where the Physics department was located.

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