Quantum Gravitational Effects and the Generalized Uncertainty Principle, Meyers, Vincent; Owens, Constance
College of Science and Mathematics
Professor: Dr. Gardo Blado
Two physical theories share between them nearly the sum of all thought given to the field of physics: General Relativity (GR) and Quantum Mechanics (QM). GR describes the behavior of the very large, and QM describes that of the very small. There has been and continues to be a great rift between them: that they appear fundamentally to disagree in their descriptions of aggregate particle interactions. The least contentious proposition to reconcile this rift increasingly appears to be the theory of Quantum Gravity (QG). It holds implications for the whole of physics, and one of the least frequently treated of these is the Minimal Length Uncertainty (MLU). Broad conjecture holds this to be on the order of the Planck Scale, or 
, though no serious effort has been devoted to ascertaining its exact size. While seemingly trivial, the fact of a MLU would dramatically restructure another of the most venerable and fundamental notions in physics, that of the Heisenberg Uncertainty Principle, which says that location and momentum are acutely related and limited. We propose that the application of QG to the Heisenberg Uncertainty Principle within the context of a finite square well is the most expeditious means of gaining an understanding of the MLU. In our research, we model the dichotomous bound and scattering states of a particle in a finite square well with a QG-corrected set of equations. Indeed, the application of QG to the uncertainty principle and the Schrödinger equation have a potentially dramatic effect on the modeled behavior of a particle in this most seminal of environments.
