Classical harmonic oscillator with quantum energy spectrum

TL;DR

This paper introduces a classical dynamical model that exhibits quantum-like energy spectra and behavior, providing a new perspective on quantum phenomena through classical systems.

Contribution

It proposes a classical variant of the harmonic oscillator that reproduces quantum energy spectra without quantum rules, offering a novel approach to quantum-classical correspondence.

Findings

The model reproduces quantum energy levels in a classical framework.

It explains regularities observed in the Franck-Hertz experiment.

Calculations align with experimental results within the proposed model.

Abstract

The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in which the Bohr-Sommerfeld quantization rule is absent and "quantum-mechanical" properties are the result of system behavior itself. For this dynamical system the classical model of Franck-Hertz experiment which allows explaining the experimentally observed regularities is suggested and investigated. The examples of calculations of Franck-Hertz experiment of within the limits of the suggested model of classical dynamical system are presented.