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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.27018 |
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| _version_ | 1866918481129111552 |
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| author | Panas, Arsen Tkachuk, Volodymyr |
| author_facet | Panas, Arsen Tkachuk, Volodymyr |
| contents | In this article, we derived a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that is physically attainable. We considered a harmonic oscillator in such a space and calculate its ground-state energy. We generalized the problem to an a sufficiently broad class of potentials, deriving an equation for the coordinate uncertainty corresponding to the minimal energy, which can be solved numerically. Using a linear approximation in the deformation parameters, we obtained a general expression for the ground-state energy. We determined the domain of existence of solutions for the anharmonic oscillator potential with respect to the deformation parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27018 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ground-state energy of a particle in a space with minimal length and minimal momentum Panas, Arsen Tkachuk, Volodymyr Quantum Physics In this article, we derived a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that is physically attainable. We considered a harmonic oscillator in such a space and calculate its ground-state energy. We generalized the problem to an a sufficiently broad class of potentials, deriving an equation for the coordinate uncertainty corresponding to the minimal energy, which can be solved numerically. Using a linear approximation in the deformation parameters, we obtained a general expression for the ground-state energy. We determined the domain of existence of solutions for the anharmonic oscillator potential with respect to the deformation parameters. |
| title | Ground-state energy of a particle in a space with minimal length and minimal momentum |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.27018 |