Classical and quantum free motions in the tomographic probability representation

TL;DR

This paper explores classical and quantum free particle motions using the tomographic probability representation, highlighting differences in their tomograms through solutions of kinetic equations.

Contribution

It introduces a geometric approach to compare classical and quantum free motions via tomograms, providing explicit solutions and analyzing their differences.

Findings

Quantum and classical tomograms differ for free particles.

Solutions of kinetic equations are obtained for both domains.

The geometric picture clarifies the distinctions between classical and quantum states.

Abstract

Based on a geometric picture, the example of free particle motion for both classical and quantum domains is considered in the tomographic probability representation. Wave functions and density operators as well as optical and symplectic tomograms are obtained as solutions of kinetic classical and quantum equations for the state tomograms. The difference of tomograms of free particle for classical and quantum states is discussed.