Analytical expressions for the transition probabilities of a molecular system interacting with a low intensity time dependent electric field are derived in the present contribution. The molecular system is modeled as a quartic anharmonic oscillator, where the interaction with the electric field is described by the electric-dipole approximation. Using Lie algebraic techniques and typical states of quantum optics, we are able to obtain an approximate analytical expression for the temporal evolution operator in the present model system. (C) 2000 Published by Elsevier Science B.V.