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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.02690 |
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Table of 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.