On position, momentum and their correlation

TL;DR

This paper investigates the correlation between position and momentum in a free quantum particle, exploring its algebraic properties, eigenvalues, and implications for wave packet dynamics and the Pauli problem.

Contribution

It introduces a detailed analysis of the correlation observable's algebra, eigenvalues, and potential role in understanding wave packet behavior and the Pauli problem in quantum mechanics.

Findings

Correlation observable's algebra and eigenvalues are characterized.

Correlation explains wave packet shrinking and spreading.

Potential relevance for solving the Pauli problem is discussed.

Abstract

Position and momentum observables are considered and their correlation is studied for the simplest quantum system of a free particle moving in one dimension. The algebra and the eigenvalue problem for the correlation observable is presented and its possible relevance for the solution of the Pauli problem is analysed. The correlation provides a simple explanation of the shrinking and spreading of wave packets in an interpretation of quantum mechanics based in an ontology suggested by quantum field theory. Several properties and speculations concerning position-momentum correlations are mentioned.