The Jaynes–Cummings model (JCM) is studied in the absence of the
rotating-wave approximation (RWA) by a coherent-state expansion technique.
In comparison with the previous paper in which the coherent-state expansion
was performed only to the third order, we carry out in this paper a complete
expansion to demonstrate exactly the dynamics of the JCM without the RWA.
Our study gives a systematic method to solve the non-RWA problem, which
would be useful in various physical systems, e.g., in a system with an
ultracold trapped ion experiencing the running waves of lasers.