  A perturbative study of the Schr\"{o}dinger equation in a strong
electromagnetic field with dipole approximation is accomplished in the
Kramers-Henneberger frame. A prove that just odd harmonics appear in the
spectrum for a linear polarized laser field is given, assuming that the atomic
radius is much lesser than the free-electron quiver motion amplitude. Within
this approximation a perturbation series is obtained in the Keldysh parameter
giving a description of multiphoton processes in the tunneling regime. The
theory is applied to the case of hydrogen-like atoms: The spectrum of higher
order harmonics and the above-threshold ionization rate are derived. The
ionization rate computed in this way determines the amplitudes of the
harmonics. The wave function of the atom proves to be rigid with respect to the
perturbation so that the effect of the laser field on the Coulomb potential in
the computation of the probability amplitudes can be neglected as a first
approximation: This approximation improves as the ratio between the amplitude
of the quiver motion of the electron and the atom radius becomes larger. The
semiclassical description currently adopted for harmonic generation is so
rederived by solving perturbatively the Schr\"{o}dinger equation.
