Year: 2025
Type: article
Abstract: This paper discusses 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.
Source: Reviews in Mathematical Physics
Authors: W. A. Zúñiga-Galindo, Nathaniel P. Mayes
Institution: The University of Texas Rio Grande Valley
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415465082