# Particle in infinite potential well with variable walls

## TL;DR

This paper explores a quantum phenomenon where a particle in an infinite potential well, after the barrier is removed, can be found with certainty at the opposite end at specific times, revealing counter-intuitive properties of quantum mechanics.

## Contribution

It introduces a thought experiment analyzing the particle's behavior in a variable-well scenario, calculating specific times of certainty based on symmetry and system parameters.

## Key findings

- Periodic certainty of particle location at specific times
- Dependence of these times on particle mass and chamber size
- Parameter ranges highlighting non-relativistic quantum mechanics limitations

## Abstract

A Gedanken experiment is described to explore a counter-intuitive property of quantum mechanics. A particle is placed in a one-dimensional infinite well. The barrier on one side of the well is suddenly removed and the chamber dramatically enlarged. At specific, periodically recurring, times the particle can be found with probability one at the opposite end of the enlarged chamber in an interval of the same size as the initial well. With the help of symmetry considerations these times are calculated and shown to be dependent on the mass of the particle and the size of the enlarged chamber. Parameter ranges are given, where the non-relativistic nature of standard quantum mechanics becomes particularly apparent.