Quantum Wave Behavior in the Presence of Finite Potential Wells

This paper explores a possible connection between quantum wave behavior and red-shift phenomena.  We begin with a detailed derivation of the transmission coefficient and use that foundation to analyze resonant photon transmission through a potential well.  In so doing, we solve for a g-factor—a dimensionless constant associated with magnetic properties—that varies along with the energy of the system in question.  Temperature dependent shifts in the g-factor relate the thermodynamic properties of blackbody radiation to a red-shift that would explain how or why the universe might be expanding.  We conclude, however, that the universe might not be expanding: instead, the universe would be filled up with potential energy wells that, along with the kinetic energy of the particle(s) they enfold, offer theoretical insight into energy transfer at both the quantum and cosmological level.  It shows that there could be a relationship between the two, and, because of that, we  might find alternative explanations for dark energy (or, for that matter, every kind of energy), that would permeate throughout the universe.