Approximately Macroscopically Unique States and Quantum Mechanics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914162710413312 |
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| author | Lin, Huaxin Wang, Hang |
| author_facet | Lin, Huaxin Wang, Hang |
| contents | We show that Mumford's Approximately Macroscopically Unique (AMU) states exist for quantum systems consisting of unbounded self-adjoint operators when the commutators are small. In particular, AMU states always exist in position and momentum systems when the Planck constant $|\hbar|$ is sufficiently small. However, we show that these standard quantum mechanical systems are far away from classical mechanical (commutative) systems even when $|\hbar|\to 0.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximately Macroscopically Unique States and Quantum Mechanics Lin, Huaxin Wang, Hang Operator Algebras We show that Mumford's Approximately Macroscopically Unique (AMU) states exist for quantum systems consisting of unbounded self-adjoint operators when the commutators are small. In particular, AMU states always exist in position and momentum systems when the Planck constant $|\hbar|$ is sufficiently small. However, we show that these standard quantum mechanical systems are far away from classical mechanical (commutative) systems even when $|\hbar|\to 0.$ |
| title | Approximately Macroscopically Unique States and Quantum Mechanics |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2510.22692 |