Uncertainty Relation for Pseudo-Hermitian Quantum Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909729267122176 |
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| author | Khantoul, Boubakeur Hamil, Bilel Benchikha, Amar |
| author_facet | Khantoul, Boubakeur Hamil, Bilel Benchikha, Amar |
| contents | This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case within a pseudo-Hermitian inner product. Analytical solutions to the time-dependent Schrödinger equation with a linearly evolving potential are derived. Furthermore, we show that the uncertainty relation for position and momentum remains real and greater than 1/2, highlighting the significance of non-Hermitian systems in quantum mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uncertainty Relation for Pseudo-Hermitian Quantum Systems Khantoul, Boubakeur Hamil, Bilel Benchikha, Amar Quantum Physics This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case within a pseudo-Hermitian inner product. Analytical solutions to the time-dependent Schrödinger equation with a linearly evolving potential are derived. Furthermore, we show that the uncertainty relation for position and momentum remains real and greater than 1/2, highlighting the significance of non-Hermitian systems in quantum mechanics. |
| title | Uncertainty Relation for Pseudo-Hermitian Quantum Systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.00648 |