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arXiv · 2410.13048

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

W. A. Zúñiga-Galindo·Nathaniel P. Mayes
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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.

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W. A. Zúñiga-Galindo, Nathaniel P. Mayes. 2024-10-16. p-Adic quantum mechanics, infinite potential wells, and continuous-time quantum walks. https://arxiv.org/abs/2410.13048

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