First researches in Physics
Majorana made substantial theoretical contributions to the group’s research, and in 1928 – while still an undergraduate – published his first paper , in which he calculated the splitting of certain spectroscopic terms in gadolinium, uranium and caesium due to the spin of the electrons. At the end of that same year, Fermi invited Majorana to give a talk at the Italian Physical Society on some applications of the Thomas–Fermi model. Then on 6 July 1929, Majorana graduated with a master degree in Physics, his dissertation was titled “The quantum theory of radioactive nuclei”.
By the end of 1931 the 25-year-old physicist had published two articles ,  on the chemical bonding of molecules and two more papers ,  on spectroscopy, one of which  anticipated results later obtained by a collaborator of Samuel Goudsmith on the “Auger effect” in helium.
In 1932, stimulated by Segrè, Majorana published an important paper  on the non-adiabatic spin-flip of atoms in a magnetic field, which was extended by Nobel laureate Rabi in 1937 and by Bloch and Rabi in 1945. This paper contained an independent derivation of the well-known Landau-Zener formula (1932) for non-adiabatic transition probability. It also introduced a novel mathematical tool for representing spherical functions (Majorana sphere), rediscovered only in recent times.
However, .the most important paper of 1932 is that concerning a Relativistic Field Theory of particles with arbitrary spin , where Majorana introduced for the first time the unitary infinite-dimensional representation of the Lorentz group. This work became a major contribution to Group Theory that has lead to key results in Theoretical Physics and anticipated analogous work by Nobel laureates Eugene Wigner in 1938 and Paul A. M. Dirac in 1945.
Due to Majorana’s peculiar character, which made him averse to publicizing his work, it is unfortunately a recurring feature of his professional life that even his published papers were not adequately known by the broader physics community.
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