# An algorithm-based introduction to the evolution of physical systems

## TL;DR

This paper introduces a simplified, algorithm-based approach to teaching the evolution of classical and quantum systems to high school students, emphasizing computational and conceptual understanding using spreadsheets.

## Contribution

It presents a novel educational method that combines numerical analysis and physics evolution equations in an accessible way for high school students.

## Key findings

- Students can compute approximate solutions to evolution equations.
- The approach highlights the role of probability in different physical contexts.
- Using spreadsheets facilitates intuitive numerical computation.

## Abstract

We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified forms of numerical analysis. The aim is to allow students to approach theoretical features as well as computational aspects of the evolution equations. In particular, the possibility to compute and analyze approximate solutions of the dynamical laws of classical, stochastic and quantum mechanics enables to highlight the distinctive role played by probability in different contexts. As computer support for numerical analysis we selected the spreadsheet. It is a work environment usually presented in high school and it is an ideal tool for an intuitive approach to numerical computation through recursive algorithms. The proposal was presented to an audience composed by students of the course of Didactics of Physics and of high school Science teachers.