Saturation effect in confined quantum systems with energy-dependent potentials
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929504457326592 |
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| author | AL-Sbaheen, Ohood Ali Al-Jamel, Ahmed Al-Masaeed, Mohamed Ghaleb |
| author_facet | AL-Sbaheen, Ohood Ali Al-Jamel, Ahmed Al-Masaeed, Mohamed Ghaleb |
| contents | In this paper, we study the saturation effect in the energy or mass spectra of three quantum models with energy-dependent potentials: the harmonic oscillator, the hydrogen atom, and the heavy quarkonia. We used the method proposed in \cite{garcia2009exactly}, which is based on studying various canonical point and gauge transformations applied to a function, $g(x)$, multiplied by a given differential equation of known solutions as special orthogonal functions, that convert it into a Schr{ö}dinger-like equation. The first two models stem from implementing the method on the confluent hypergeometric differential of the well-known solutions ${}_1 F_1$, while the third model (heavy quarkonia) stems possibly from the hypergeometric differential of the well-known solutions ${}_2 F_1$. In particular, the heavy quarkonia mass spectra for both $c\bar c$ and $b\bar b$ are produced at different values of the saturation parameter $λ$ and compared with the available experimental data. It is found that these systems may exhibit saturation effect when the energy-dependent effect is included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Saturation effect in confined quantum systems with energy-dependent potentials AL-Sbaheen, Ohood Ali Al-Jamel, Ahmed Al-Masaeed, Mohamed Ghaleb Quantum Physics In this paper, we study the saturation effect in the energy or mass spectra of three quantum models with energy-dependent potentials: the harmonic oscillator, the hydrogen atom, and the heavy quarkonia. We used the method proposed in \cite{garcia2009exactly}, which is based on studying various canonical point and gauge transformations applied to a function, $g(x)$, multiplied by a given differential equation of known solutions as special orthogonal functions, that convert it into a Schr{ö}dinger-like equation. The first two models stem from implementing the method on the confluent hypergeometric differential of the well-known solutions ${}_1 F_1$, while the third model (heavy quarkonia) stems possibly from the hypergeometric differential of the well-known solutions ${}_2 F_1$. In particular, the heavy quarkonia mass spectra for both $c\bar c$ and $b\bar b$ are produced at different values of the saturation parameter $λ$ and compared with the available experimental data. It is found that these systems may exhibit saturation effect when the energy-dependent effect is included. |
| title | Saturation effect in confined quantum systems with energy-dependent potentials |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.00302 |