Abstract
The point-to-point Feynman quantum propagator ⟨q1|exp(−iHt/ℏ)|q2⟩ has an analytic form only for quadratic potentials. We apply the split operator approach to obtain a propagator matrix for arbitrary potentials for non-uniform grids, which are particularly useful for real physical potentials with both rapid-varying and smooth regions. We exemplify our method with the wave propagation function and the extraction of an eigenvalue and an eigenfunction of a Morse system modelling diatomic molecules.