Application of RWA leads to false conclusions about the transition probability for the near or exact resonance

Rotating wave approximation (RWA) plays a key rule in quantum optics to solve some Schr\"{o}dinger equation approximately. For example, it is well known that RWA has been used to calculate the transition probability. However, so far no one shows the validity of RWA. Recently Larson [J. Larson, Phys. Rev. Lett. 108, 033601 (2012)] gave the first example showing that the application of RWA in the Jaynes-Cummings model may lead to false conclusions. In this paper, we analytically and numerically show that the application of RWA leads to false conclusions about the transition probability for the near or exact resonance.
Comment: 14 pages, 2 figures This paper has been withdrawn by the authors because Eq. (22) holds only for some case and the figures ploted from the data obtained with 15*10^{6} iterations are not precice. The figures will be ploted with 15*10^{8}iterations to solve the ode by using workstation