Levinson’s theorem is generalized to quantum scattering with time-periodic potentials. The zero-energy limit of the phase shift in the elastic channel is linked to the number of bound (cyclic) states of the time-dependent potential by the same relation as in the static case.

Martin, Ph. A. and Sassoli de Bianchi, M. (1996). Levinson’s theorem for time-periodic potentials. Europhys. Lett. 34, pp. 639-643. Doi: 10.1209/epl/i1996-00508-7.