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

TL;DR

This paper revisits Majorana's early work on non-adiabatic transitions, deriving the Landau-Zener formula and providing a full wave function including phase, with implications for quantum control and information.

Contribution

It rederives the Landau-Zener transition probability using Majorana's approach and extends it to include the full wave function with phase information.

Findings

Derivation of the Landau-Zener transition probability from Majorana's method

Full wave function including phase for nonadiabatic transitions

Asymptotic wave function accurately describes dynamics far from crossing

Abstract

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-St\"{u}ckelberg-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, St\"{u}ckelberg. 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.