The Jaynes-Cummings model describing the interaction of a single linearly p
olarized mode of the quantized electromagnetic field with an isolated two-l
evel atom is generalized to the case of atomic levels degenerate in the pro
jections of the angular momenta on the quantization axis, which is a usual
case in the experiments. This generalization, like the original model, obta
ins the explicit solution. The model is applied to calculate the dependence
of the cavity field characteristics on the angle between the polarization
of the cavity field mode and that of the laser excitation pulse in the expe
riment with one-atom micromaser. It is shown that the polarization of the e
xcitation pulse may be varied to govern the cavity field parameters, for ex
ample, to increase the average number of photons in the cavity or to switch
the photon statistics from sub- to super-Poissonian.