Infinite square well and periodic trajectories in classical mechanics

TL;DR

This paper explores the classical dynamics of a particle in an infinite square well, analyzing periodic trajectories through Hamiltonian and Hamilton-Jacobi formalisms to deepen understanding of confined motion.

Contribution

It introduces a detailed classical analysis of the infinite square well using Hamiltonian and Hamilton-Jacobi equations, highlighting periodic trajectories and their characteristics.

Findings

Periodic motion inside the well is characterized and illustrated.

Hamiltonian and Hamilton-Jacobi equations effectively describe the dynamics.

Examples demonstrate the nature of confined classical trajectories.

Abstract

We examine the classical problem of an infinite square well by considering Hamilton's equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of suitable examples, the nature of the periodic motion of a particle trapped inside the well.