We explore the possibility of modifying the Lewis-Riesenfeld method ofin-variants developed originally to find exact solutions for time-dependent quantum me-chanical systems for the situation in which an exact invariant can beconstructed, butthe subsequently resulting time-independent eigenvalue system is not solvable exactly.We propose to carry out this step in an approximate fashion, such as employing stan-dard time-independent perturbation theory or the WKB approximation, and subsequentlyfeeding the resulting approximated expressions back into the time-dependent scheme. Weillustrate the quality of this approach by contrasting an exactly solvable solution to oneobtained with a perturbatively carried out second step for two types of explicitly time-dependent optical potential
