A comprehensive introduction to the basic formalism of the one-dimensional scattering by time-periodic short-ranged potentials is presented. The fundamental objects of the theory (transmission and reflexion probabilities, sidebands and time delays) are defined, and a generalized Born expansion derived. Particular emphasis is given to the connection between the time-dependent approach and the quasi-stationary one. In particular, the independence of the scattering process of the choice of time-origin, in the limit of a monoenergetic wave packet, is clearly established. The generalized Born expansion is applied to two archetypical models: the square barrier with modulated height (the celebrated Büttiker-Landauer model) and the square barrier with oscillating position. For these two models, the full transmission probability is calculated up to the first non-vanishing correction in the time-dependent perturbation.

Sassoli de Bianchi, M. & Saraga, D. (1997). On the One-Dimensional Scattering by Time-Periodic Potentials: General Theory and Application to Specific Models. Helv. Phys. Acta 70, pp. 751-779. Doi: 10.5169/seals-117049.