An algebraic approach to gravitational quantum mechanics
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915294067294208 |
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| author | Chung, Won Sang Junker, Georg Hassanabadi, Hassan |
| author_facet | Chung, Won Sang Junker, Georg Hassanabadi, Hassan |
| contents | Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of Heisenberg's algebra resulting in a generalized uncertainty principle and constitute what is called gravitational quantum mechanics. Utilizing the position representation of this deformed algebra, we study various models of gravitational quantum mechanics. The free time evolution of a Gaussian wave packet is investigated as well as the spectral properties of a particle bound by an external attractive potential. Here the cases of a box with infinite walls and an attractive potential well of finite depth are considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17626 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An algebraic approach to gravitational quantum mechanics Chung, Won Sang Junker, Georg Hassanabadi, Hassan General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Quantum Physics Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of Heisenberg's algebra resulting in a generalized uncertainty principle and constitute what is called gravitational quantum mechanics. Utilizing the position representation of this deformed algebra, we study various models of gravitational quantum mechanics. The free time evolution of a Gaussian wave packet is investigated as well as the spectral properties of a particle bound by an external attractive potential. Here the cases of a box with infinite walls and an attractive potential well of finite depth are considered. |
| title | An algebraic approach to gravitational quantum mechanics |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2402.17626 |