A quantum mechanical discussion of Rabi oscillations

In 1937, Rabi treated the problem of a magnetic moment in an applied time-dependent magnetic field. This became the well-known magnetic resonance situation. The Hamiltonian is often taken to be (II) over cap = -mu.[B-0(k) over cap + B-1(t)(i) over cap]. In this paper, the Rabi oscillations formula, describing the spin flipping, is derived in an unusual way. The method uses a modification of a method due to Heitler. In the Heitler method, one uses the Interaction Picture of quantum mechanics. Due to the time-dependence in the problem, the usual Heitler method fails. However, the solution is found after quantizing the electromagnetic field. To better understand the origin of the spin flipping, the analogous time-independent problem is also solved. It is made clear that the origin of the Rabi oscillations is not due to the time-dependent magnetic field. The spin flipping is essentially due to the fact that the spin system, when initially prepared, is not in an eigenstate of the Hamiltonian. Thus, as times progresses, the system naturally evolves through the noneigenstate basis states.