  Discrepancies and accords between quantum (QM) and classical mechanics (CM)
related to expectation values and periods are found for both the simple
harmonic oscillator (SHO) and a free particle in a box (FPB), which may apply
generally. These indicate non-locality is expected throughout QM. The FPB
energy states violate the Correspondence Principle. Previously unexpected
accords are found and proven that the classical and quantum expectation values
are the same for the expectation value of the second moment and the beat period
(i.e. beats between the phases for adjoining energy states) for the SHO for all
quantum numbers, n. However, for the FPB the beat periods differ significantly
at small n. It is shown that a particle's velocity in an infinite square well
varies, no matter how wide the box, nor how far the particle is from the walls.
The quantum free particle variances 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. The concept of an "Expectation Value over a Partial
Well Width" is introduced. This paper raises the question as to whether these
inconsistencies are undetectable, or can be empirically ascertained. These
inherent variances may need to be fixed, or nature is manifestly more
non-classical than expected.
