Position probability density function for a system of mutually exclusive particles in one dimension

TL;DR

This paper defines the position probability density function for mutually exclusive particles in one dimension, explores quantum limitations, and applies classical correspondence principles to continuous mass densities.

Contribution

It introduces a new framework for describing mutually exclusive particles' position probabilities and extends the concept to continuous mass densities using the correspondence principle.

Findings

Quantum particles at finite potentials are not mutually exclusive or distinguishable.

The position probability distribution can be defined for mutually exclusive particles.

Application of the correspondence principle to continuous mass densities.

Abstract

Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at finite potentials can not be regarded as a mutually exclusive system or they are indistinguishable. Afterward, it is attempted to ascribe a mutually exclusive system to continuous mass densities of a rigid body to calculate average values. We do this by applying correspondence principle with regard to probability densities.