Theory of quantum resonance: A renormalization-group approach

The standard perturbation theory for time-dependent problems in quantum mechanics is reconsidered through renormalization-group methods. This approach justifies a posteriori the theory of quantum resonance given by the multiple-scale analysis of the perturbation series applied to the coupled equations of wavefunction amplitudes. The resonance equations for the leading-order amplitude probabilties are then obtained up to second order and a general method for the algorithmic computation of higher-order terms of the perturbation series is given. The three-level model in a monochromatic wave with two resonant states is discussed in the light of the present results.