Recursive Schrödinger equation approach to faster converging path integrals.

By recursively solving the underlying Schrödinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this, we obtain discrete short-time propagators for both one and many particles in arbitrary dimension to orders that have not been accessible before. They can be used to substantially speed up numerical Monte Carlo calculations of path integrals, as well as for setting up an alternative analytical approximation scheme for energy spectra, density of states, and other statistical properties of quantum systems.