Chirped laser pulses equation

A. The Dressed Schrodinger Equation for Chirped Laser Pulses... 

We first derive the time-dependent dressed Schrodinger equation generated by the Floquet Hamiltonian, relevant for processes induced by chirped laser pulses (see Section IV.A). The adiabatic principles to solve this equation are next described in Section IV.B. 

Equations (7)-(9) are well suited for numerical evaluation with arbitrary functions defining the spatial and temporal distributions of the laser pulse. In addition, the system (7)-(9) is rather convenient for analytical treatment. In particular, one can develop further perturbative expansion of (7)-(8) in terms of the fine structure constant a. In the leading order, this yields nonrelativistic formulas which agree with those formerly derived by us in [19]. For unchirped laser signals (i.e., t) = 0) these reduce further to the result of [31] by expanding all quantities in powers of the laser intensity I(r,t). Extensive numerical tests carried out by us for various forms of the chirp pulse en-... 

---