Quantum and Classical Variance in the Quantum Realm

TL;DR

This paper explores the variances in quantum and classical predictions, revealing subtle effects and raising questions about quantum consistency and the non-classical nature of reality, with specific analysis on harmonic oscillators and particle systems.

Contribution

It introduces new insights into quantum and classical variances, highlighting phenomena analogous to Aharonov-Bohm effects and examining quantum self-inconsistency.

Findings

Quantum and classical variances share indirect commonalities with Aharonov-Bohm effects.

Significant variances are found in harmonic oscillator and particle in a box systems.

The second spatial moment for the harmonic oscillator is identical in quantum and classical mechanics.

Abstract

This paper examines the variance of quantum and classical predictions in the quantum realm, as well as unexpected presence and absence of variances. Some features are found that share an indirect commonality with the Aharonov-Bohm and Aharonov-Casher effects in that there is a quantum action in the absence of a force. Variances are also found in the presence of a force that are more subtle as they are of higher order. Significant variances related to the harmonic oscillator and particle in a box periods are found. This paper raises the question whether apparent quantum self-inconsistency may be examined internally, or must be empirically ascertained. These inherent variances may either point to inconsistencies in quantum mechanics that should be fixed, or that nature is manifestly more non-classical than expected. For the harmonic oscillator it is proven that the second spatial moment is the same in QM and CM.