p-Adic quantum mechanics, infinite potential wells, and continuous-time quantum walks
Abstract
This article 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 Schr\"odinger 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.
Cite
@article{arxiv.2410.13048,
title = {p-Adic quantum mechanics, infinite potential wells, and continuous-time quantum walks},
author = {W. A. Zúñiga-Galindo and Nathaniel P. Mayes},
journal= {arXiv preprint arXiv:2410.13048},
year = {2024}
}
Comments
The paper was fully revisited. Two new sections were added. arXiv admin note: text overlap with arXiv:2308.01283