Derivation of the Rabi Equation by Means of the Pauli Matrices

Abstract: The general quantum-mechanical properties of two-level systems are very relevant for the study of different physical subjects of great interest, as, for instance, magnetic resonance, nuclear physics, molecular dynamics, masers, neutrino oscillations, quantum computation, etc. In this work we present a nonperturbative approach to the study of the oscillations among two quantum states when an interaction term is considered. First, we show that using a simple parametrization for the superposition of the two states, it is possible to derive easily the Rabi equation. Next, we show that the Pauli matrices can be conveniently used to write the Hamiltonian operator and to derive the Rabi equation, directly applying the time evolution operator to the initial state of the system