Quantum particle on the surface of a spherocylindrical capsule
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910822644580352 |
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| author | Poorkahnooji, Elham Mazharimousavi, S. Habib |
| author_facet | Poorkahnooji, Elham Mazharimousavi, S. Habib |
| contents | A spinless nonrelativistic quantum particle on the curved surface of a homogeneous spherocylindrical capsule is considered. We apply Costa's formalism to solve the Schrödinger equation with only a confined potential forcing the particle to remain on the surface and be free to move. It is shown that while a quantum particle with zero tangential/local energy can exist on the surface of a spherical shell with an arbitrary radius, it exists on a spherocylinder capsule only with a quantized length-to-radius ratio. In other words, if and only if the length-to-radius ratio of the capsule is an even multiplication of $π$, the wave function on the surface interferes with itself constructively such that the wave function survives. This hypothetical phenomenon may lead to applications in nanoscale measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum particle on the surface of a spherocylindrical capsule Poorkahnooji, Elham Mazharimousavi, S. Habib General Physics A spinless nonrelativistic quantum particle on the curved surface of a homogeneous spherocylindrical capsule is considered. We apply Costa's formalism to solve the Schrödinger equation with only a confined potential forcing the particle to remain on the surface and be free to move. It is shown that while a quantum particle with zero tangential/local energy can exist on the surface of a spherical shell with an arbitrary radius, it exists on a spherocylinder capsule only with a quantized length-to-radius ratio. In other words, if and only if the length-to-radius ratio of the capsule is an even multiplication of $π$, the wave function on the surface interferes with itself constructively such that the wave function survives. This hypothetical phenomenon may lead to applications in nanoscale measurements. |
| title | Quantum particle on the surface of a spherocylindrical capsule |
| topic | General Physics |
| url | https://arxiv.org/abs/2409.13737 |