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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/2404.01881 |
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| _version_ | 1866914954125246464 |
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| author | Mostafazadeh, Ali |
| author_facet | Mostafazadeh, Ali |
| contents | We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general the Hamiltonian operator does not represent an observable of the system even if it is a self-adjoint operator. This is related to a hidden geometric aspect of quantum mechanics arising from the presence of an operator-valued gauge potential. We also offer a careful treatment of quantum systems whose Hilbert space is obtained by endowing a time-independent vector space with a time-dependent inner product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consistent treatment of quantum systems with a time-dependent Hilbert space Mostafazadeh, Ali Quantum Physics General Relativity and Quantum Cosmology Mathematical Physics We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general the Hamiltonian operator does not represent an observable of the system even if it is a self-adjoint operator. This is related to a hidden geometric aspect of quantum mechanics arising from the presence of an operator-valued gauge potential. We also offer a careful treatment of quantum systems whose Hilbert space is obtained by endowing a time-independent vector space with a time-dependent inner product. |
| title | Consistent treatment of quantum systems with a time-dependent Hilbert space |
| topic | Quantum Physics General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2404.01881 |