Date of Award
Doctor of Philosophy
Thomas Papenbrock, Robert Hinde, Norman Mannella
Uncertainty estimates in theoretical physics are just as important as they are in experimental physics. As a theorist, one must qualify a given calculation with the assumptions on which the calculation is performed. Such a practice equips the scientific community with the context necessary to evaluate the validity of a theory. It also provides some basis upon which the theory can develop improvements. The work presented here concerns itself with two sources of uncertainty in theoretical physics. First, we discuss numerical uncertainties. Particularly, we quantify the uncertainties introduced by basis truncations and the exploit it to extrapolate infinite-basis results. Second, we examine framework uncertainties — those attributable to the inherent failure of the employed model to describe the fullness of nature. We establish the sufficiency of a two-body contact interaction to renormalize short-distance physics in the two- and three-body sectors of systems where singular potentials relevant to nuclear and atomic dominate the low-energy behavior.
Odell, Daniel Jr, "Uncertainty Estimates in Few-Body Physics. " PhD diss., University of Tennessee, 2019.