Wave functions for the regular pentagonal two-dimensional quantum box and thin microstrip antenna
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917223309770752 |
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| author | Langhorne, Tristan Domenech, Erik E. Gonzalez, Juan Oliveros Klemm, Richard A. |
| author_facet | Langhorne, Tristan Domenech, Erik E. Gonzalez, Juan Oliveros Klemm, Richard A. |
| contents | The general wave functions for the two-dimensional regular pentagonal quantum box and thin microstrip antenna are derived. As for the square, equilateral triangular, and circular disk-shaped boxes and antennas, there are two quantum nunbers $n$ and $m$. In those cases, $n\ge1 $ and $m\ge 0$ are both unlimited non-negative integers of any value. For the regular pentagon, only $n\ge1 $ is an unlimited positive quantum number, but $m_{\rm min}\le m\le 5$, where $m_{\rm min}=0$ for the pentagonal microstrip antenna with Neumann boundary conditions and $m_{\rm min}=1$ for the pentagonal quantum box with Dirichlet boundary conditions. Color-coded pictures of the wave functions for the regular pentagonal quantum box and microstrip antenna are presented for all allowed $m$ values and for $1\le n\le 2$ and for the microstrip antenna for all allowed $m$ values and $n=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17925 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wave functions for the regular pentagonal two-dimensional quantum box and thin microstrip antenna Langhorne, Tristan Domenech, Erik E. Gonzalez, Juan Oliveros Klemm, Richard A. Superconductivity The general wave functions for the two-dimensional regular pentagonal quantum box and thin microstrip antenna are derived. As for the square, equilateral triangular, and circular disk-shaped boxes and antennas, there are two quantum nunbers $n$ and $m$. In those cases, $n\ge1 $ and $m\ge 0$ are both unlimited non-negative integers of any value. For the regular pentagon, only $n\ge1 $ is an unlimited positive quantum number, but $m_{\rm min}\le m\le 5$, where $m_{\rm min}=0$ for the pentagonal microstrip antenna with Neumann boundary conditions and $m_{\rm min}=1$ for the pentagonal quantum box with Dirichlet boundary conditions. Color-coded pictures of the wave functions for the regular pentagonal quantum box and microstrip antenna are presented for all allowed $m$ values and for $1\le n\le 2$ and for the microstrip antenna for all allowed $m$ values and $n=3$. |
| title | Wave functions for the regular pentagonal two-dimensional quantum box and thin microstrip antenna |
| topic | Superconductivity |
| url | https://arxiv.org/abs/2601.17925 |