Canonical description of quantum dynamics

TL;DR

This paper explores a geometric reformulation of quantum mechanics in phase space, providing intuitive insights into non-classical effects through properties of quantum moments and their dynamics.

Contribution

It introduces a phase-space framework for quantum states and dynamics, linking uncertainty relations to geometric barriers, offering a novel perspective on quantum non-classicality.

Findings

Phase-space properties of quantum moments analyzed

Geometrical interpretation of uncertainty relations

Equivalence between uncertainty conditions and centrifugal barriers

Abstract

Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents various phase-space properties of moments describing a quantum state and its dynamics. An example of a geometrical reformulation of a non-classical quantum effect is given by an equivalence between conditions imposed by uncertainty relations and centrifugal barriers, respectively.