Quantum-dressed classical mechanics: Theory and application

Abstract

A new method called “quantum dressed” classical mechanics has been formulated for treating problems within molecular dynamics, i.e. inelastic and reactive collisions, photodissociation, molecule–surface dynamics, non-adiabatic transitions etc. The method is based on an expansion of the wavefunction in a time-dependent basis set, the Gauss–Hermite basis set. From here it is possible to construct a discrete variable representation in which the grid points are defined by the Hermite part of the Gauss–Hermite basis set. The formulation introduces a set of grid points which follow the classical trajectory in space. With enough grid points the method approaches the exact quantum mechanical formulation. With just a single grid point in each dimension, we recover classical mechanics. Hence the new method adds a quantum option to ordinary Newtonian mechanics.