  Radio-frequency quantum engineering of spins is based on the dressing by a
non resonant electromagnetic field. Radio-frequency dressing occurs also for
the motion of particles, electrons or ultracold atoms, within a periodic
spatial potential. The dressing, producing a renormalisation and also a freeze
of the system energy, is described by different approaches, dressed atom,
magnetic resonance semiclassical treatment, continued fraction solution of the
Schr\"odinger equation. A comparison between those solutions points out that
the semiclassical treatment, to be denoted as the $S$-solution, represents the
most convenient tool to evaluate the tunneling renormalization of ultracold
atoms.
