Quantum-mechanical treatment of two particles in a potential box

TL;DR

This paper explores the quantum behavior of two distinguishable particles in a potential box, revealing that quantum principles restrict their possible positions to discrete points, contrasting classical physics.

Contribution

It introduces a quantum-mechanical model for two particles in a box, analyzing how quantum principles alter classical positional constraints.

Findings

Particles are confined to discrete positions in the quantum model

Quantum principles modify classical positional restrictions

The model provides insights into quantum localization phenomena

Abstract

In classical physics, there is a basic principle, namely "A particle cannot be located at the position of another one on the same time". Which consequences can be derived if this principle is transferred into quantum physics? For doing that, two distinguishable particles are considered to be trapped in a potential box by means of the Schr\"odinger equation. In result, the particles can necessarily be located only at discrete positions.