Beyond the Eikonal Approximation in Classical Optics and Quantum Physics

Abstract

In this chapter, a glimpse of the way how the concept of quantumtrajectories has been used in different areas of quantum chemistryand chemical physics is provided. Putting aside ontological issues,Bohmian mechanics has been exploited within these fields withpractical purposes, both analytical and computational. Analytically,although quantum trajectories provide the same information ata predictive level as standard quantum mechanics, they havethe advantage that one can follow and describe the evolution ofquantum systems by means of streamlines, whose results are lessvague and more intuitive than standard wave packet simulations.On the other hand, computationally, Bohmian mechanics has beenthe source of a number of numerical algorithms devised as analternative to other methods based on the wave function or theprobability density. This will be seen throughout the analysisand discussion of different applications, which go from electronicstructure to chemical dynamics, thus covering essentially theresearch spectrum of quantum chemistry and chemical physics.Furthermore, in the form of a final summary, we present a unifyingscheme based on minimum principles, which allows us to connectelectronic structurewith classical and quantum (Bohmian) chemicaldynamics.