Quantum and Classical Variance in the Quantum Realm

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.