Splitting the wavefunctions of two particles in two boxes

TL;DR

This paper investigates how splitting the wavefunctions of two identical quantum particles in separate boxes affects their final positions, providing insights into measurement and phase information for bosons and fermions.

Contribution

It offers a novel analysis of wavefunction splitting and particle exchange in two-particle quantum systems, including solutions for bosons and fermions.

Findings

Provides a method to determine particle positions after wavefunction splitting.

Defines a measurement to extract phase information from split wavefunctions.

Analyzes differences between bosonic and fermionic particle behavior.

Abstract

I consider two identical quantum particles in two boxes. We can split each box, and thereby the wavefunction of each particle, into two parts. When two half boxes are interchanged and combined with the other halves, where do the two particles end up? I solve this problem for two identical bosons and for two identical fermions. The solution can be used to define a measurement that yields some information about the relative phase between the two parts of a split wavefunction.