A harmonic oscillator may display a nonlinear behavior when forced by an inhomogeneous field. We calculate the response of harmonic molecules adsorbed on a surface to a monochromatic electric field employing algebraic methods. The field inhomogeneity, due to image effects, produces harmonics which we evaluate non-perturbatively as a function of the intensity and frequency of the field and the distance to the substrate. We compare the results with those obtained using perturbation theory.
Transition probabilities between quantum states of a molecular system interacting with a low intensity time dependent field were obtained. The molecular system is modeled as a quartic anharmonic oscillator, whereas the interaction with the electric field is described by the electric-dipole approximation. We apply Lie algebraic techniques and make use of iterative Bogoliubov transformations to derive an approximate expression for the evolution operator. The methodological procedure proposed by Yuen allows us to evaluate the final time evolution operator in a closed for, using the optical properties of the two- photon coherent state of the radiation field.
Transition probabilities and mean property values of a molecular systems interacting with a low-intensity electromagnetic field are studied by algebraic methods developed in a the present contribution. Lie algebra and a harmonic-oscillator description is used as a first characterization of the system. The SU(2) algebra is used later to characterize the same harmonic system in the dipolar classical approximation for the radiation-matter interaction.