Hybrid mechanics: A combination of classical and quantum mechanics

Abstract

Because classical mechanics is so much easier to handle than quantum mechanics, the time evolution of wave functions for molecular dynamics is often calculated using semiclassical methods. The errors of such methods grow, in general, faster than linearly with time, although they may be quite small for small, but finite times. We therefore propose to use a semiclassical method to calculate the quantum mechanical time propagator for a finite time step (say 1/10 of a vibrational period) and to use this propagator and quantum mechanics for longer times. To describe the quantum time propagator we use a basis set that can describe regions in phase space that are not necessarily rectangular, but can have any shape, that will become important in applications to higher dimensions. We give numerical examples to demonstrate the accuracy of the method.