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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.06325 |
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| _version_ | 1866913384027389952 |
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| author | Moscato, Antonio |
| author_facet | Moscato, Antonio |
| contents | This paper studies a system of $n \in \mathbb{N}: \, n \geq 2$ non-relativistic, spinless quantum particles moving on the real line and interacting via a two-body delta potential. The Hamiltonian of such a system is proved to be affiliated to the resolvent algebra of the case, $\mathcal{R}\left( \mathbb{R}^{2n},σ\right)$; it is further shown the existence of a $\text{C}^{\ast}-$dynamical system and of a subalgebra $π_S\left( \mathfrak{S}_0 \right)^{-1} \subset \mathcal{R}\left( \mathbb{R}^{2n},σ\right)$, stable under time evolution, where $π_S$ is the Schr{ö}dinger representation of the algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | n Distinguishable Particles on the Real Line interacting via Two Body Delta Potentials Moscato, Antonio Mathematical Physics This paper studies a system of $n \in \mathbb{N}: \, n \geq 2$ non-relativistic, spinless quantum particles moving on the real line and interacting via a two-body delta potential. The Hamiltonian of such a system is proved to be affiliated to the resolvent algebra of the case, $\mathcal{R}\left( \mathbb{R}^{2n},σ\right)$; it is further shown the existence of a $\text{C}^{\ast}-$dynamical system and of a subalgebra $π_S\left( \mathfrak{S}_0 \right)^{-1} \subset \mathcal{R}\left( \mathbb{R}^{2n},σ\right)$, stable under time evolution, where $π_S$ is the Schr{ö}dinger representation of the algebra. |
| title | n Distinguishable Particles on the Real Line interacting via Two Body Delta Potentials |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2406.06325 |