Harmonic potential as an effective limit of a discrete classical interaction

TL;DR

This paper investigates how a simple classical discrete interaction model can effectively approximate the continuous harmonic oscillator, shedding light on the quantum-to-classical transition and drawing parallels with gravity.

Contribution

It introduces a discrete interaction model for the harmonic oscillator and explores its limit towards continuous behavior, providing insights into the quantum-classical transition.

Findings

Discrete model approaches continuous harmonic oscillator behavior

Parallel drawn between discrete interactions and gravity

Enhanced understanding of quantum-to-classical transition

Abstract

Motivated by improving the understanding of the quantum-to-classical transition we use a simple model of classical discrete interactions for studying the discrete-to-continuous transition in the classical harmonic oscillator. A parallel is traced with gravity for stressing the relevance of such discrete interaction models.