Jordan Algebraic Formulation of Quantum Mechanics and The Non-commutative Landau Problem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916160003375104 |
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| author | Dereli, Tekin Yörük, Ekin Sıla |
| author_facet | Dereli, Tekin Yörük, Ekin Sıla |
| contents | We present a Jordan algebraic formulation of the non-commutative Landau problem coupled to a harmonic potential. To achieve this, an alternative formulation of the Hilbert space version of quantum mechanics is presented. Using this construction, the Hilbert space corresponding to the non-commutative Landau problem is obtained. Non-commutative parameters are then described in terms of an associator in the Jordan algebraic setting. Pure states and density matrices arising from this problem are characterized. This in turn leads us to the Jordan-Schrödinger time-evolution equation for the state vectors for this specific problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12047 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Jordan Algebraic Formulation of Quantum Mechanics and The Non-commutative Landau Problem Dereli, Tekin Yörük, Ekin Sıla Quantum Physics Mathematical Physics We present a Jordan algebraic formulation of the non-commutative Landau problem coupled to a harmonic potential. To achieve this, an alternative formulation of the Hilbert space version of quantum mechanics is presented. Using this construction, the Hilbert space corresponding to the non-commutative Landau problem is obtained. Non-commutative parameters are then described in terms of an associator in the Jordan algebraic setting. Pure states and density matrices arising from this problem are characterized. This in turn leads us to the Jordan-Schrödinger time-evolution equation for the state vectors for this specific problem. |
| title | Jordan Algebraic Formulation of Quantum Mechanics and The Non-commutative Landau Problem |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2312.12047 |