p-Adic quantum mechanics, infinite potential wells, and continuous-time quantum walks
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910743452975104 |
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| author | Zúñiga-Galindo, W. A. Mayes, Nathaniel P. |
| author_facet | Zúñiga-Galindo, W. A. Mayes, Nathaniel P. |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | p-Adic quantum mechanics, infinite potential wells, and continuous-time quantum walks Zúñiga-Galindo, W. A. Mayes, Nathaniel P. Quantum Physics 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 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. |
| title | p-Adic quantum mechanics, infinite potential wells, and continuous-time quantum walks |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.13048 |