Recursive Schr\" odinger Equation Approach to Faster Converging Path Integrals

TL;DR

This paper introduces a recursive Schrödinger equation method to derive high-order discretized effective actions, significantly enhancing the efficiency of path integral calculations and analytical approximations in quantum systems.

Contribution

It presents a novel recursive approach for deriving analytic expressions for discretized effective actions, enabling faster and more accurate path integral computations.

Findings

Derived discrete short-time propagators for multiple particles in arbitrary dimensions.

Achieved higher-order effective actions previously inaccessible.

Demonstrated potential for speeding up Monte Carlo path integral calculations.

Abstract

By recursively solving the underlying Schr\" odinger 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 which 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 a new analytical approximation scheme for energy spectra, density of states, and other statistical properties of quantum systems.