We have formulated a new way of making quantum corrections to classical mechanics. The method is based on a time-dependent discrete variable representation (DVR) of the wave function with grid points 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.