Approximation of Schrödinger eigenvalues and eigenfunctions by canonical perturbation theory: The periodically driven quantum rotator

Abstract

A first-order approximate formula for eigenvalues and eigenfunctions of the Schrödinger operator of the periodically driven quantum rotator is given by means of the classical perturbation theory and an estimate for the remainder is provided; in the nonresonant case the remainder is of order 2 while in the resonant case the remainder turns out to be of order 3/2. In the first case, to what extent the procedure can be interated to higher orders is also discussed.