p-Adic quantum mechanics, infinite potential wells, and continuous-time quantum walks

Authors

• Wilson A. Zuniga-Galindo, The University of Texas Rio Grande ValleyFollow
• Nathaniel P. Mayes, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

7-1-2026

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.

Comments

Free Access  

Recommended Citation

Zúniga-Galindo, W. A., and Nathaniel P. Mayes. "p-Adic quantum mechanics, infinite potential wells, and continuous-time quantum walks." Reviews in Mathematical Physics 38, no. 06 (2026): 2550027. https://doi.org/10.1142/S0129055X25500278

Publication Title

Reviews in Mathematical Physics

DOI

10.1142/S0129055X25500278