Quantum Propagator for Arbitrary Potentials on General Grids

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 wavefunction propagation and the extraction of an eigenvalue and an eigenfunction of a Morse system modelling diatomic molecules.