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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2511.16053 |
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| _version_ | 1866910247089602560 |
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| author | Walsh, Connor MacPherson, Ian Joseph, Davidson Kabra, Suyash Toor, Ripanjeet Singh Protter, Mason Marsiglio, Frank |
| author_facet | Walsh, Connor MacPherson, Ian Joseph, Davidson Kabra, Suyash Toor, Ripanjeet Singh Protter, Mason Marsiglio, Frank |
| contents | We describe a simple quantum dot that consists of two crossed two-dimensional troughs. As such there is no potential well; nonetheless, this geometry gives rise to a bound state, centred on the point at which these troughs cross one another. This problem is interesting both because the existence of a bound state may surprise students and because it can be solved using a variety of computational techniques, including matrix mechanics, finite differences, and mode matching. We present these methods and show how the mode-matching method in this case provides the most accurate solution to the problem. Additionally, the mode-matching method can be used to generate a simple wave function that yields the lowest energy known to date to arise out of an analytical variational solution for this problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A simple quantum dot: numerical and variational solutions Walsh, Connor MacPherson, Ian Joseph, Davidson Kabra, Suyash Toor, Ripanjeet Singh Protter, Mason Marsiglio, Frank Mesoscale and Nanoscale Physics We describe a simple quantum dot that consists of two crossed two-dimensional troughs. As such there is no potential well; nonetheless, this geometry gives rise to a bound state, centred on the point at which these troughs cross one another. This problem is interesting both because the existence of a bound state may surprise students and because it can be solved using a variety of computational techniques, including matrix mechanics, finite differences, and mode matching. We present these methods and show how the mode-matching method in this case provides the most accurate solution to the problem. Additionally, the mode-matching method can be used to generate a simple wave function that yields the lowest energy known to date to arise out of an analytical variational solution for this problem. |
| title | A simple quantum dot: numerical and variational solutions |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2511.16053 |