Regularized quantum motion in a bounded set: Hilbertian aspects
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914831263596544 |
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| author | Bagarello, Fabio Gazeau, Jean-Pierre Trapani, Camillo |
| author_facet | Bagarello, Fabio Gazeau, Jean-Pierre Trapani, Camillo |
| contents | It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous set of self-adjoint extensions. We prove that essential self-adjointness can be recovered by symmetrically weighting the momentum operator with a positive bounded function approximating the indicator function of the considered interval. This weighted momentum operator is consistently obtained from a similarly weighted classical momentum through the so-called Weyl-Heisenberg covariant integral quantization of functions or distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularized quantum motion in a bounded set: Hilbertian aspects Bagarello, Fabio Gazeau, Jean-Pierre Trapani, Camillo Mathematical Physics Quantum Physics It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous set of self-adjoint extensions. We prove that essential self-adjointness can be recovered by symmetrically weighting the momentum operator with a positive bounded function approximating the indicator function of the considered interval. This weighted momentum operator is consistently obtained from a similarly weighted classical momentum through the so-called Weyl-Heisenberg covariant integral quantization of functions or distributions. |
| title | Regularized quantum motion in a bounded set: Hilbertian aspects |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2406.06989 |