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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.16292 |
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| _version_ | 1866918030172225536 |
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| author | Nakazato, Hiromichi Ozawa, Tohru |
| author_facet | Nakazato, Hiromichi Ozawa, Tohru |
| contents | The time-dependent free Schrödinger operator is shown to be characterized as the only linear partial differential operator of the second order that is invariant under the Galilei group in the Euclidean space-time $\mathbb R\times\mathbb R^n$. The method of proof depends on the analysis of the invariance of polynomials given by the application of the linear partial differential operators to monochromatic plane waves under space rotations and pure Galilei transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16292 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of the time-dependent free Schrödinger operator by the Galilei invariance Nakazato, Hiromichi Ozawa, Tohru Mathematical Physics The time-dependent free Schrödinger operator is shown to be characterized as the only linear partial differential operator of the second order that is invariant under the Galilei group in the Euclidean space-time $\mathbb R\times\mathbb R^n$. The method of proof depends on the analysis of the invariance of polynomials given by the application of the linear partial differential operators to monochromatic plane waves under space rotations and pure Galilei transformations. |
| title | Characterization of the time-dependent free Schrödinger operator by the Galilei invariance |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2505.16292 |