Propagator of Quantum Systems in the Probability Representation

TL;DR

This paper derives the evolution equation for the optical propagator in quantum systems and explores its relation to the quantum propagator, especially for quadratic systems, within the probability representation framework.

Contribution

It introduces the evolution equation for the optical propagator and explicitly relates it to the quantum propagator for quadratic systems, advancing the probability representation approach.

Findings

Derived the evolution equation for the optical propagator.

Established explicit relations between optical and quantum propagators.

Applied results to quadratic systems in quantum mechanics.

Abstract

The evolution equation for the propagator of the quantum system in the optical probability representation (optical propagator) is obtained. The relations between the optical and quantum propagators for the Schr\"odinger equation and the optical propagator of an arbitrary quadratic system are found explicitly.