  Using techniques of complex analysis in an algebraic approach, we solve the
wave equation for a two-level atom interacting with a monochromatic light field
exactly. A closed-form expression for the quasi-energies is obtained, which
shows that the Bloch-Siegert shift is always finite, regardless of whether the
original or the shifted level spacing is an integral multiple of the driving
frequency, $\omega$. We also find that the wave functions, though finite when
the original level spacing is an integral multiple of $\omega$, become
divergent when the intensity-dependent shifted energy spacing is an integral
multiple of the photon energy. This result provides, for the first time in the
literature, an ab-initio theoretical explanation for the occurrence of the
Freeman resonances observed in above-threshold ionization experiments.
