Wave function of classical particle in linear potential

TL;DR

This paper explores the classical particle in a linear potential using Hilbert space formalism and tomographic probability, solving the Liouville equation through a wave function-based density matrix and discussing quantum relations.

Contribution

It introduces a novel approach applying quantum-like Hilbert space methods to classical mechanics in a linear potential context.

Findings

Solution of Liouville equation via wave function density matrix

Establishment of quantum-classical relation in this formalism

Representation of classical dynamics in a quantum-like framework

Abstract

The problem of classical particle in linear potential is studied by using the formalism of Hilbert space and tomographic probability distribution. The Liouville equation for this problem is solved by finding the density matrix satisfying von Newmann-like equation in the form of product of wave functions. The relation to quantum mechanics is discussed.