  The solution of a two level system driven by a Laser in the adiabatic limit
is determined using third order Magnus expansion. We made the assumption that
the laser is on resonance or close to resonance with the Bohr transition. As a
consequence of which we are able to obtain a Hamiltonian which commute with
itself at different times. We solve the problem using the Sylvester Formula
where we make use of the eigenvalues.
