23 June 2022 Thu 4 pm

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Schroedinger's paper on an undulatory description of microscopic phenomena dates back to 1926. In the same year, a correspondence between stationary quantum states and invariant tori was independently devised by Wentzel, Brillouin and Krammers based on O(ℏ) expansions. Two years later, van Vleck used the same approach to link quantum and classical dynamics for any system, without requiring the existence of phase-space tori. Since these approximations both reproduce quantum interference and are written exclusively in terms of classical quantities, they were dubbed semiclassical and extensively employed as geometrical guides in the analysis of simple quantum phenomena. With the advent of the modern computer in the 1980s, Hamilton's equations could be finally integrated and semiclassical mechanics would now provide quantitative results for much more complex systems, especially in quantum chemistry.

In this talk, the mathematical formalism of semiclassical propagation will be briefly described, with an emphasis in the transition between pure van Vleck-Maslov-Gutzwiller theory and the more modern Initial and Final Value Representation techniques. Some case studies will be presented where semiclassical methods can successfully reproduce quantum dynamics, while simultaneously providing illuminating interpretations. It will then be argued that, as is already the case in chemistry, it is time for semiclassical physics to turn into a serious computational tool and be used to investigate high-dimensional problems, for which solving Schroedinger's equation is computationally hopeless.

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