Application of quantum-dressed classical mechanics: Molecule surface scattering

Quantum corrections to classical mechanics can be formulated by a new method called quantum-dressed classical mechanics. The method is based on a time-dependent discrete variable representation (DVR) of the wave function. The grid points are defined by the Hermite part of a basis set, the Gauss-Hermite basis set. The formulation introduces a set of grid points which follow the classical trajectory in space. With enough trajectories (DVR points), the method approaches the exact quantum formulation. With just a single grid point in each dimension, we recover classical mechanics. The method is, in the present paper, used to treat the dynamics of molecule surface interaction.