p-Adic Quantum Mechanics, Infinite Potential Wells, and Continuous-Time Quantum Walks

Author

Nathaniel P. Mayes, The University of Texas Rio Grande Valley

Date of Award

5-2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Wilson Zúñiga-Galindo

Second Advisor

Sergey Grigorian

Third Advisor

Timothy Huber

Abstract

In this thesis, we introduce a p-adic version of the infinite potential well in quantum mechanics (QM). This model describes the confinement of a particle in a p-adic ball. We rigorously solve the Cauchy problem for the Schrödinger equation and determine the stationary solutions. The p-adic balls are fractal objects. By dividing a p-adic ball into a finite number of sub-balls and using the wavefunctions of the infinite potential well, we construct a continuous-time quantum walk (CTQW) on a fully connected graph, where each vertex corresponds to a sub-ball in the partition of the original ball. In this way, we establish a connection between p-adic QM and quantum computing. This thesis is based on [71].

Comments

Copyright 2025 Nathaniel P. Mayes. https://proquest.com/docview/3240636040

Recommended Citation

Mayes, N. (2025). p-Adic Quantum Mechanics, Infinite Potential Wells, and Continuous-Time Quantum Walks [Doctoral dissertation, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/1716