  A well-known method of transferring the population of a quantum system from
an eigenspace of the free Hamiltonian to another is to use a periodic control
law with an angular frequency equal to the difference of the eigenvalues. For
finite dimensional quantum systems, the classical theory of averaging provides
a rigorous explanation of this experimentally validated result. This paper
extends this finite dimensional result, known as the Rotating Wave
Approximation, to infinite dimensional systems and provides explicit
convergence estimates.
