J. C. A. Barata
Converging Perturbative Solutions of the Schroedinger Equation for a 
Two-Level System with a Hamiltonian Depending Periodically on Time
(357K, Postscript)

ABSTRACT.  We study the Schroedinger equation of a class of two-level systems 
under the action of a periodic time-dependent external field in the 
situation where the energy difference 2epsilon between the free energy 
levels is sufficiently small with respect to the strength of the 
external interaction. Under suitable conditions we show that this 
equation has a solution in terms of converging power series expansions 
in epsilon. In contrast to other expansion methods, like in the Dyson 
expansion, the method we present is not plagued by the presence of 
``secular terms''. Due to this feature we were able to prove absolute 
and uniform convergence of the Fourier series involved in the 
computation of the wave functions and to prove absolute convergence 
of the epsilon-expansions leading to the ``secular frequency'' and to 
the coefficients of the Fourier expansion of the wave function.