The forced harmonic oscillator: Coherent states and the RWA

We consider a forced harmonic oscillator in one-dimension. Using coherent states, we show that the treatment of the system is simplified, that the relationship between the classical and quantum solutions becomes transparent, and that the evolution operator of the system can be calculated easily as the free evolution operator of the harmonic oscillator followed by a displacement operator that depends on the classical solution. In addition, we consider the system in the rotating-wave-approximation (RWA), an application of the Averaging Theorem. We determine the relationship between the exact solution and the one in the RWA, test the accuracy of the RWA, and explain why the RWA gives accurate results in the realm of cavity quantum electrodynamics. Finally, we apply the results to a charged particle interacting with an electromagnetic field.