Majorana's approach to nonadiabatic transitions validates the adiabatic-impulse approximation

The approach by Ettore Majorana for non-adiabatic transitions between two quasi-crossing levels is revisited. We rederive the transition probability, known as the Landau-Zener-Stückelberg-Majorana formula, and introduce Majorana’s approach to modern readers. This result typically referred as the Landau-Zener formula, was published by Majorana before Landau, Zener, Stückelberg. Moreover, we obtain the full wave function, including its phase, which is important nowadays for quantum control and quantum information. The asymptotic wave function correctly describes dynamics far from the avoided-level crossing, while it has limited accuracy in that region.