The time-dependent wave operator formalism is used to describe the quantum dynamics of molecular systems. It is shown that the wave function, if correctly normalized at each moment of time, is the solution of an ''instantaneous eigenvalue equation.'' This result is verified in the case of an harmonic oscillator with a linear perturbation. It is further shown that the resulting time-dependent ''eigenvalue'' can be used to obtain the eigenvalues of the Floquet eigenvectors participating in the dynamics, and constituting the target space of the system. This is illustrated by a numerical example, concerning the photodissociation of the H-2(+) ion in a continuous electromagnetic field. (C) 1997 American Institute of Physics.