The Feynman effective classical potential in the Schr\"odinger formulation

TL;DR

This paper explores the connection between Feynman path integrals and the Schrödinger formulation by analyzing the effective classical potential, providing new insights into statistical mechanics and dynamical approximations.

Contribution

It introduces a comprehensive formulation linking the effective classical potential to the quasi-static response in the Schrödinger framework, enhancing understanding of dynamical approximations.

Findings

The effective classical potential relates to the system's response to external forces.

New physical insights into path integral and Schrödinger correspondence.

Framework for dynamical approximations based on the effective potential.

Abstract

New physical insight into the correspondence between path integral concepts and the Schr\"odinger formulation is gained by the analysis of the effective classical potential, that is defined within the Feynman path integral formulation of statistical mechanics. This potential is related to the quasi-static response of the equilibrium system to an external force. These findings allow for a comprehensive formulation of dynamical approximations based on this potential.