On formal quasi-periodic solutions of the Schrodinger equation for a two-level system with a Hamiltonian depending quasi-periodically on time

We consider the Schrodinger equation for a class of two-level atoms in a quasi-periodic external field for large coupling, i.e. for which the energy difference 2 epsilon between the unperturbed levels is sufficiently small. We show that this equation has a solution in terms of a formal power series in epsilon, with coefficients which are quasi-periodical functions of the time, in analogy to the Lindstedt-Poincare series in classical mechanics.