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

Solution of two level system using $3^{rd}$ order Magnus expansion