COMING SOON! PQDT Open is getting a new home!

ProQuest Open Access Dissertations & Theses will remain freely available as part of a new and enhanced search experience at www.proquest.com.

Questions? Please refer to this FAQ.

Dissertation/Thesis Abstract

An Update on the Computational Theory of Hamiltonian Period Functions
by Klee, Bradley Joseph, Ph.D., University of Arkansas, 2020, 189; 28259376
Abstract (Summary)

Lately, state-of-the-art calculation in both physics and mathematics has expanded to include the field of symbolic computing. The technical content of this dissertation centers on a few Creative Telescoping algorithms of our own design (Mathematica implementations are given as a supplement). These algorithms automate analysis of integral period functions at a level of difficulty and detail far beyond what is possible using only pencil and paper (unless, perhaps, you happen to have savant-level mental acuity). We can then optimize analysis in classical physics by using the algorithms to calculate Hamiltonian period functions as solutions to ordinary differential equations. The simple pendulum is given as an example where our ingenuity contributes positively to developing the exact solution, and to non-linear data analysis. In semiclassical quantum mechanics, period functions are integrated to obtain action functions, which in turn contribute to an optimized procedure for estimating energy levels and their splittings. Special attention is paid to a comparison of the effectiveness of quartic and sextic double wells, and an insightful new analysis is given for the semiclassical asymmetric top. Finally we conclude with a minor revision of Harter's original analysis of semi-rigid rotors with Octahedral and Icosahedral symmetry.

Supplemental Files

Some files may require a special program or browser plug-in. More Information

Indexing (document details)
Advisor: Harter, William G.
Commitee: Kennefick, Daniel J., Barraza-Lopez, Salvador, Harriss, Edmund O.
School: University of Arkansas
Department: Physics
School Location: United States -- Arkansas
Source: DAI-A 82/8(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Computer science, Design, Information Technology, Applied physics, Applied Mathematics
Keywords: Algebraic goemetry, Creative telescoping, Hamiltonian mechanics, Semiclassical mechanics, Energy level estimation
Publication Number: 28259376
ISBN: 9798569978120
Copyright © 2021 ProQuest LLC. All rights reserved. Terms and Conditions Privacy Policy Cookie Policy
ProQuest