Demonstrating two-particle interference with a one-dimensional delta potential well

TL;DR

This paper presents a simple, visualizable model of two-particle interference using a one-dimensional delta potential well to illustrate the Hong-Ou-Mandel effect and exchange symmetry effects for different particle types.

Contribution

It introduces a concrete, easy-to-understand model for two-particle interference that can be used for educational purposes, contrasting with more abstract quantum descriptions.

Findings

Derived conditions for the Hong-Ou-Mandel effect using wave packet evolution.

Demonstrated interference differences among bosons, fermions, and distinguishable particles.

Provided a visualizable model suitable for classroom teaching.

Abstract

In quantum mechanics, the exchange symmetry of wave functions for identical particles has observable effects, including the widely studied Hong-Ou-Mandel (HOM) effect. A theoretical description using second quantization is elegant but abstract. In contrast, this paper describes a simple model of two-particle interference using a one-dimensional delta potential well as a beam splitter. The conditions for the HOM effect are derived from the perspective of wave packet evolution. Furthermore, the interference processes of bosons, fermions and distinguishable particles are demonstrated and compared in detail. The method presented here is concrete, easy to visualize, and can help students to better understand the effects arising from the exchange symmetry of wave functions. The main results can be animated for classroom teaching or developed into an undergraduate seminar topic.