A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912710948552704 |
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| author | de Lucas, Javier Lange, Julia Rivas, Xavier |
| author_facet | de Lucas, Javier Lange, Julia Rivas, Xavier |
| contents | By using the theory of analytic vectors and manifolds modelled on normed spaces, we provide a rigorous symplectic differential geometric approach to $t$-dependent Schrödinger equations on separable (possibly infinite-dimensional) Hilbert spaces determined by unbounded $t$-dependent self-adjoint Hamiltonians satisfying a technical condition. As an application, the Marsden--Weinstein reduction procedure is employed to map above-mentioned $t$-dependent Schrödinger equations onto their projective spaces. Other applications of physical and mathematical relevance are also analysed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09192 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting de Lucas, Javier Lange, Julia Rivas, Xavier Mathematical Physics Differential Geometry Quantum Physics 34A26, 34A34 (primary) 17B66, 53Z05 (secondary) By using the theory of analytic vectors and manifolds modelled on normed spaces, we provide a rigorous symplectic differential geometric approach to $t$-dependent Schrödinger equations on separable (possibly infinite-dimensional) Hilbert spaces determined by unbounded $t$-dependent self-adjoint Hamiltonians satisfying a technical condition. As an application, the Marsden--Weinstein reduction procedure is employed to map above-mentioned $t$-dependent Schrödinger equations onto their projective spaces. Other applications of physical and mathematical relevance are also analysed. |
| title | A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting |
| topic | Mathematical Physics Differential Geometry Quantum Physics 34A26, 34A34 (primary) 17B66, 53Z05 (secondary) |
| url | https://arxiv.org/abs/2312.09192 |