Effects of position-dependent mass (PDM) on the bound-state solutions of a massive spin-0 particle subjected to the Yukawa potential
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913571824205824 |
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| author | Oliveira, P. H. F. Lima, W. P. |
| author_facet | Oliveira, P. H. F. Lima, W. P. |
| contents | With the advent of Albert Einstein's theory of special relativity, Klein and Gordon made the first attempt to elevate time to the status of a coordinate in the Schrödinger equation. In this study, we graphically discuss the eigenfunctions and eigenenergies of the Klein-Gordon equation with a Yukawa-type potential (YP), within a position-dependent mass (PDM) framework. We conclude that the PDM leads to the equivalence of the positive ($E^+$) and negative ($E^-$) solution states at low energies. We observe that in the energy spectrum as a function of $η$ (YP intensity factor), the PDM can induce gap closure at the critical point where $E^+$ and $E^-$ become imaginary. In the spectrum as a function of $α$ (YP shielding factor), it can compel the energies to be zero at $α=0$, instead of being equal to $(m_0c^2)$ as in the invariant mass case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02690 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effects of position-dependent mass (PDM) on the bound-state solutions of a massive spin-0 particle subjected to the Yukawa potential Oliveira, P. H. F. Lima, W. P. Quantum Physics High Energy Physics - Theory With the advent of Albert Einstein's theory of special relativity, Klein and Gordon made the first attempt to elevate time to the status of a coordinate in the Schrödinger equation. In this study, we graphically discuss the eigenfunctions and eigenenergies of the Klein-Gordon equation with a Yukawa-type potential (YP), within a position-dependent mass (PDM) framework. We conclude that the PDM leads to the equivalence of the positive ($E^+$) and negative ($E^-$) solution states at low energies. We observe that in the energy spectrum as a function of $η$ (YP intensity factor), the PDM can induce gap closure at the critical point where $E^+$ and $E^-$ become imaginary. In the spectrum as a function of $α$ (YP shielding factor), it can compel the energies to be zero at $α=0$, instead of being equal to $(m_0c^2)$ as in the invariant mass case. |
| title | Effects of position-dependent mass (PDM) on the bound-state solutions of a massive spin-0 particle subjected to the Yukawa potential |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.02690 |