  For studying the dynamics of a two-level system coupled to a quantum
oscillator we have presented an analytical approach, the transformed
rotating-wave approximation, which takes into account the effect of the
counter-rotating terms but still keeps the simple mathematical structure of the
ordinary rotating-wave approximation. We have calculated the energy levels of
ground and lower-lying excited states, as well as the time-dependent quantum
dynamics. It is obvious that the approach is quite simple and can be easily
extended to more complicated situation. Besides, the results are compared with
the numerically exact ones to show that for weak and intermediate coupling and
moderate detuning our analytic calculations are quantitatively in good
agreement with the exact ones.
