Introduction to the Rotating Wave Approximation (RWA) : Two Coherent Oscillations

In this note I introduce a mysterious approximation called the rotating wave approximation (RWA) to undergraduates or non-experts who are interested in both Mathematics and Quantum Optics. In Quantum Optics it plays a very important role in order to obtain an analytic approximate solution of some Schr{"o}dinger equation, while it is curious from the mathematical point of view. I explain it carefully with two coherent oscillations for them and expect that they will overcome the problem in the near future.