The approach by Ettore Majorana for non-adiabatic transitions between two quasi-crossing levels is revisited and significantly extended. 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 and Stückelberg. Moreover, we go well beyond previous results and we now obtain the full wave function, including its phase, which is important nowadays for quantum control and quantum information. The asymptotic wave function correctly describes the dynamics away from the avoided-level crossing, while it has limited accuracy in that region.

The article studies the elastic and locomotive properties of Miuraori-type paper origami. The mechanics of a single paper crease is studied experimentally, and its non-elastic properties turn out to be crucial. The entire origami construction is then described as a collection of individual creases, its capability to launch small objects is evaluated, and the equation of motion is found. Thus, the height of the launched ball is studied theoretically and experimentally as a function of governing parameters.